diff --git a/toolchain/check/handle_alias.cpp b/toolchain/check/handle_alias.cpp
index f93d80721044..f07da27793fe 100644
--- a/toolchain/check/handle_alias.cpp
+++ b/toolchain/check/handle_alias.cpp
@@ -46,29 +46,16 @@ auto HandleParseNode(Context& context, Parse::AliasId /*node_id*/) -> bool {
       {.name_id = name_context.name_id_for_new_inst(),
        .parent_scope_id = name_context.parent_scope_id});
 
-  auto alias_type_id = SemIR::TypeId::None;
-  auto alias_value_id = SemIR::InstId::None;
-  if (auto inst = context.insts().TryGetAs<SemIR::NameRef>(expr_id)) {
-    // Pass through name references, albeit changing the name in use.
-    alias_type_id = inst->type_id;
-    alias_value_id = inst->value_id;
-  } else if (auto inst =
-                 context.insts().TryGetAs<SemIR::TypeLiteral>(expr_id)) {
-    // Treat type literals such as `type` or `bool` like name references.
-    alias_type_id = inst->type_id;
-    alias_value_id = inst->value_id;
-  } else {
-    CARBON_DIAGNOSTIC(AliasRequiresNameRef, Error,
-                      "alias initializer must be a name reference");
-    context.emitter().Emit(expr_node, AliasRequiresNameRef);
-    alias_type_id = SemIR::ErrorInst::TypeId;
-    alias_value_id = SemIR::ErrorInst::InstId;
+  if (!context.constant_values().Get(expr_id).is_constant()) {
+    CARBON_DIAGNOSTIC(AliasRequiresConstantValue, Error,
+                      "alias refers to a runtime value");
+    context.emitter().Emit(expr_node, AliasRequiresConstantValue);
   }
-  auto alias_id =
-      AddInst<SemIR::AliasBinding>(context, name_context.loc_id,
-                                   {.type_id = alias_type_id,
-                                    .entity_name_id = entity_name_id,
-                                    .value_id = alias_value_id});
+  auto alias_id = AddInst<SemIR::AliasBinding>(
+      context, name_context.loc_id,
+      {.type_id = context.insts().Get(expr_id).type_id(),
+       .entity_name_id = entity_name_id,
+       .value_id = expr_id});
 
   // Add the name of the binding to the current scope.
   context.decl_name_stack().PopScope();
diff --git a/toolchain/check/testdata/alias/basics.carbon b/toolchain/check/testdata/alias/basics.carbon
index fb12584e0478..a34359719aad 100644
--- a/toolchain/check/testdata/alias/basics.carbon
+++ b/toolchain/check/testdata/alias/basics.carbon
@@ -35,6 +35,18 @@ alias c = b;
 let d: c = {};
 //@dump-sem-ir-end
 
+// --- alias_to_generic.carbon
+
+library "[[@TEST_NAME]]";
+
+class A(T:! type) {}
+
+//@dump-sem-ir-begin
+alias a = A({});
+//@dump-sem-ir-end
+
+let v: a = {} as A({});
+
 // --- fail_control_flow.carbon
 
 library "[[@TEST_NAME]]";
@@ -82,7 +94,7 @@ library "[[@TEST_NAME]]";
 var a: () = ();
 var b: ()* = &a;
 
-// CHECK:STDERR: fail_not_constant.carbon:[[@LINE+4]]:11: error: alias initializer must be a name reference [AliasRequiresNameRef]
+// CHECK:STDERR: fail_not_constant.carbon:[[@LINE+4]]:11: error: alias refers to a runtime value [AliasRequiresConstantValue]
 // CHECK:STDERR: alias c = *b;
 // CHECK:STDERR:           ^~
 // CHECK:STDERR:
@@ -92,14 +104,10 @@ alias c = *b;
 
 library "[[@TEST_NAME]]";
 
-// CHECK:STDERR: fail_params.carbon:[[@LINE+8]]:8: error: `alias` declaration cannot have parameters [UnexpectedDeclNameParams]
+// CHECK:STDERR: fail_params.carbon:[[@LINE+4]]:8: error: `alias` declaration cannot have parameters [UnexpectedDeclNameParams]
 // CHECK:STDERR: alias A(T:! type) = T*;
 // CHECK:STDERR:        ^~~~~~~~~~
 // CHECK:STDERR:
-// CHECK:STDERR: fail_params.carbon:[[@LINE+4]]:21: error: alias initializer must be a name reference [AliasRequiresNameRef]
-// CHECK:STDERR: alias A(T:! type) = T*;
-// CHECK:STDERR:                     ^~
-// CHECK:STDERR:
 alias A(T:! type) = T*;
 
 // --- fail_modifiers.carbon
@@ -155,7 +163,7 @@ extern alias C = Class;
 // CHECK:STDOUT:
 // CHECK:STDOUT: file {
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %c: type = alias_binding c, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %c: type = alias_binding c, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -176,11 +184,11 @@ extern alias C = Class;
 // CHECK:STDOUT:
 // CHECK:STDOUT: file {
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %a: type = alias_binding a, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %a: type = alias_binding a, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %a.ref: type = name_ref a, %a [concrete = constants.%C]
-// CHECK:STDOUT:   %b: type = alias_binding b, %a [concrete = constants.%C]
+// CHECK:STDOUT:   %b: type = alias_binding b, %a.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %b.ref: type = name_ref b, %b [concrete = constants.%C]
-// CHECK:STDOUT:   %c: type = alias_binding c, %b [concrete = constants.%C]
+// CHECK:STDOUT:   %c: type = alias_binding c, %b.ref [concrete = constants.%C]
 // CHECK:STDOUT:   name_binding_decl {
 // CHECK:STDOUT:     %d.patt: %pattern_type = value_binding_pattern d [concrete]
 // CHECK:STDOUT:   }
@@ -199,3 +207,26 @@ extern alias C = Class;
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
+// CHECK:STDOUT: --- alias_to_generic.carbon
+// CHECK:STDOUT:
+// CHECK:STDOUT: constants {
+// CHECK:STDOUT:   %A.type: type = generic_class_type @A [concrete]
+// CHECK:STDOUT:   %A.generic: %A.type = struct_value () [concrete]
+// CHECK:STDOUT:   %empty_struct_type: type = struct_type {} [concrete]
+// CHECK:STDOUT:   %empty_struct: %empty_struct_type = struct_value () [concrete]
+// CHECK:STDOUT:   %A.ed7: type = class_type @A, @A(%empty_struct_type) [concrete]
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: file {
+// CHECK:STDOUT:   %A.ref: %A.type = name_ref A, %A.decl [concrete = constants.%A.generic]
+// CHECK:STDOUT:   %.loc7_14: %empty_struct_type = struct_literal () [concrete = constants.%empty_struct]
+// CHECK:STDOUT:   %.loc7_15: type = converted %.loc7_14, constants.%empty_struct_type [concrete = constants.%empty_struct_type]
+// CHECK:STDOUT:   %A: type = class_type @A, @A(constants.%empty_struct_type) [concrete = constants.%A.ed7]
+// CHECK:STDOUT:   %a: type = alias_binding a, %A [concrete = constants.%A.ed7]
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: fn @__global_init() {
+// CHECK:STDOUT: !entry:
+// CHECK:STDOUT:   <elided>
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
diff --git a/toolchain/check/testdata/alias/builtins.carbon b/toolchain/check/testdata/alias/builtins.carbon
index 9f3f96669b4c..e9e4c93844b4 100644
--- a/toolchain/check/testdata/alias/builtins.carbon
+++ b/toolchain/check/testdata/alias/builtins.carbon
@@ -26,18 +26,13 @@ library "[[@TEST_NAME]]";
 alias b = bool;
 //@dump-sem-ir-end
 
-// --- fail_bool_value.carbon
+// --- bool_value.carbon
 
 library "[[@TEST_NAME]]";
 
 //@dump-sem-ir-begin
-// CHECK:STDERR: fail_bool_value.carbon:[[@LINE+4]]:11: error: alias initializer must be a name reference [AliasRequiresNameRef]
-// CHECK:STDERR: alias a = false;
-// CHECK:STDERR:           ^~~~~
-// CHECK:STDERR:
 alias a = false;
 
-// This fails silently due to the above diagnostic.
 let a_test: bool = a;
 //@dump-sem-ir-end
 
@@ -50,17 +45,17 @@ let a_test: bool = a;
 // CHECK:STDOUT:
 // CHECK:STDOUT: file {
 // CHECK:STDOUT:   %i32: type = type_literal constants.%i32 [concrete = constants.%i32]
-// CHECK:STDOUT:   %a: type = alias_binding a, constants.%i32 [concrete = constants.%i32]
+// CHECK:STDOUT:   %a: type = alias_binding a, %i32 [concrete = constants.%i32]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- bool.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: file {
 // CHECK:STDOUT:   %.loc5: type = type_literal bool [concrete = bool]
-// CHECK:STDOUT:   %b: type = alias_binding b, bool [concrete = bool]
+// CHECK:STDOUT:   %b: type = alias_binding b, %.loc5 [concrete = bool]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: --- fail_bool_value.carbon
+// CHECK:STDOUT: --- bool_value.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %false: bool = bool_literal false [concrete]
@@ -69,17 +64,17 @@ let a_test: bool = a;
 // CHECK:STDOUT:
 // CHECK:STDOUT: file {
 // CHECK:STDOUT:   %false: bool = bool_literal false [concrete = constants.%false]
-// CHECK:STDOUT:   %a: <error> = alias_binding a, <error> [concrete = <error>]
+// CHECK:STDOUT:   %a: bool = alias_binding a, %false [concrete = constants.%false]
 // CHECK:STDOUT:   name_binding_decl {
 // CHECK:STDOUT:     %a_test.patt: %pattern_type.831 = value_binding_pattern a_test [concrete]
 // CHECK:STDOUT:   }
-// CHECK:STDOUT:   %.loc12: type = type_literal bool [concrete = bool]
-// CHECK:STDOUT:   %a_test: bool = value_binding a_test, <error> [concrete = <error>]
+// CHECK:STDOUT:   %.loc7: type = type_literal bool [concrete = bool]
+// CHECK:STDOUT:   %a_test: bool = value_binding a_test, @__global_init.%a.ref
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
 // CHECK:STDOUT: !entry:
-// CHECK:STDOUT:   %a.ref: <error> = name_ref a, file.%a [concrete = <error>]
+// CHECK:STDOUT:   %a.ref: bool = name_ref a, file.%a [concrete = constants.%false]
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/alias/export_name.carbon b/toolchain/check/testdata/alias/export_name.carbon
index 636fcbfec298..1c41c13c0b26 100644
--- a/toolchain/check/testdata/alias/export_name.carbon
+++ b/toolchain/check/testdata/alias/export_name.carbon
@@ -96,7 +96,7 @@ var d: D* = &c;
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
diff --git a/toolchain/check/testdata/alias/import.carbon b/toolchain/check/testdata/alias/import.carbon
index f7bf468a7b7b..0c46d44be0e0 100644
--- a/toolchain/check/testdata/alias/import.carbon
+++ b/toolchain/check/testdata/alias/import.carbon
@@ -105,7 +105,7 @@ var c: () = a_alias_alias;
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref.loc6: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %c_alias: type = alias_binding c_alias, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %c_alias: type = alias_binding c_alias, %C.ref.loc6 [concrete = constants.%C]
 // CHECK:STDOUT:   name_binding_decl {
 // CHECK:STDOUT:     %a.patt: %pattern_type.506 = ref_binding_pattern a [concrete]
 // CHECK:STDOUT:     %a.var_patt: %pattern_type.506 = var_pattern %a.patt [concrete]
@@ -185,7 +185,7 @@ var c: () = a_alias_alias;
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %default.import = import <none>
 // CHECK:STDOUT:   %c_alias.ref.loc6: type = name_ref c_alias, imports.%Main.c_alias [concrete = constants.%C]
-// CHECK:STDOUT:   %c_alias_alias: type = alias_binding c_alias_alias, imports.%Main.c_alias [concrete = constants.%C]
+// CHECK:STDOUT:   %c_alias_alias: type = alias_binding c_alias_alias, %c_alias.ref.loc6 [concrete = constants.%C]
 // CHECK:STDOUT:   name_binding_decl {
 // CHECK:STDOUT:     %b.patt: %pattern_type.506 = ref_binding_pattern b [concrete]
 // CHECK:STDOUT:     %b.var_patt: %pattern_type.506 = var_pattern %b.patt [concrete]
@@ -324,7 +324,7 @@ var c: () = a_alias_alias;
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %a: ref %empty_tuple.type = ref_binding a, %a.var [concrete = %a.var]
 // CHECK:STDOUT:   %a.ref: ref %empty_tuple.type = name_ref a, %a [concrete = %a.var]
-// CHECK:STDOUT:   %a_alias: ref %empty_tuple.type = alias_binding a_alias, %a [concrete = %a.var]
+// CHECK:STDOUT:   %a_alias: ref %empty_tuple.type = alias_binding a_alias, %a.ref [concrete = %a.var]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -367,7 +367,7 @@ var c: () = a_alias_alias;
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %default.import = import <none>
 // CHECK:STDOUT:   %a_alias.ref: ref %empty_tuple.type = name_ref a_alias, imports.%Main.a_alias [concrete = imports.%a.var]
-// CHECK:STDOUT:   %a_alias_alias: ref %empty_tuple.type = alias_binding a_alias_alias, imports.%Main.a_alias [concrete = imports.%a.var]
+// CHECK:STDOUT:   %a_alias_alias: ref %empty_tuple.type = alias_binding a_alias_alias, %a_alias.ref [concrete = imports.%a.var]
 // CHECK:STDOUT:   name_binding_decl {
 // CHECK:STDOUT:     %b.patt: %pattern_type = ref_binding_pattern b [concrete]
 // CHECK:STDOUT:     %b.var_patt: %pattern_type = var_pattern %b.patt [concrete]
diff --git a/toolchain/check/testdata/alias/import_access.carbon b/toolchain/check/testdata/alias/import_access.carbon
index c51ddcf7ae16..d8bc4895d4ca 100644
--- a/toolchain/check/testdata/alias/import_access.carbon
+++ b/toolchain/check/testdata/alias/import_access.carbon
@@ -71,7 +71,7 @@ var inst: Test.A = {};
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %A: type = alias_binding A, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %A: type = alias_binding A, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
diff --git a/toolchain/check/testdata/alias/import_order.carbon b/toolchain/check/testdata/alias/import_order.carbon
index 22257486f1ae..9b446449921f 100644
--- a/toolchain/check/testdata/alias/import_order.carbon
+++ b/toolchain/check/testdata/alias/import_order.carbon
@@ -54,13 +54,13 @@ var a_val: a = {.v = b_val.v};
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %a: type = alias_binding a, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %a: type = alias_binding a, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %a.ref: type = name_ref a, %a [concrete = constants.%C]
-// CHECK:STDOUT:   %b: type = alias_binding b, %a [concrete = constants.%C]
+// CHECK:STDOUT:   %b: type = alias_binding b, %a.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %b.ref: type = name_ref b, %b [concrete = constants.%C]
-// CHECK:STDOUT:   %c: type = alias_binding c, %b [concrete = constants.%C]
+// CHECK:STDOUT:   %c: type = alias_binding c, %b.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %c.ref: type = name_ref c, %c [concrete = constants.%C]
-// CHECK:STDOUT:   %d: type = alias_binding d, %c [concrete = constants.%C]
+// CHECK:STDOUT:   %d: type = alias_binding d, %c.ref [concrete = constants.%C]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
diff --git a/toolchain/check/testdata/alias/in_namespace.carbon b/toolchain/check/testdata/alias/in_namespace.carbon
index 544978ed36e9..c9c3b84b9976 100644
--- a/toolchain/check/testdata/alias/in_namespace.carbon
+++ b/toolchain/check/testdata/alias/in_namespace.carbon
@@ -34,14 +34,10 @@ library "[[@TEST_NAME]]";
 namespace NS;
 
 fn F() -> {} {
-  // CHECK:STDERR: fail_local_in_namespace.carbon:[[@LINE+8]]:9: error: name `NS` not found [NameNotFound]
+  // CHECK:STDERR: fail_local_in_namespace.carbon:[[@LINE+4]]:9: error: name `NS` not found [NameNotFound]
   // CHECK:STDERR:   alias NS.a = {};
   // CHECK:STDERR:         ^~
   // CHECK:STDERR:
-  // CHECK:STDERR: fail_local_in_namespace.carbon:[[@LINE+4]]:16: error: alias initializer must be a name reference [AliasRequiresNameRef]
-  // CHECK:STDERR:   alias NS.a = {};
-  // CHECK:STDERR:                ^~
-  // CHECK:STDERR:
   alias NS.a = {};
   // CHECK:STDERR: fail_local_in_namespace.carbon:[[@LINE+4]]:10: error: member name `a` not found in `NS` [MemberNameNotFoundInInstScope]
   // CHECK:STDERR:   return NS.a;
@@ -62,7 +58,7 @@ fn F() -> {} {
 // CHECK:STDOUT:     .a = %a
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %a: type = alias_binding a, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %a: type = alias_binding a, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/alias/local.carbon b/toolchain/check/testdata/alias/local.carbon
deleted file mode 100644
index 71fdae002559..000000000000
--- a/toolchain/check/testdata/alias/local.carbon
+++ /dev/null
@@ -1,38 +0,0 @@
-// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
-// Exceptions. See /LICENSE for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-// INCLUDE-FILE: toolchain/testing/testdata/min_prelude/destroy.carbon
-//
-// AUTOUPDATE
-// TIP: To test this file alone, run:
-// TIP:   bazel test //toolchain/testing:file_test --test_arg=--file_tests=toolchain/check/testdata/alias/local.carbon
-// TIP: To dump output, run:
-// TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/check/testdata/alias/local.carbon
-
-// --- local.carbon
-
-library "[[@TEST_NAME]]";
-
-fn F() -> () {
-  var a: () = ();
-  //@dump-sem-ir-begin
-  alias b = a;
-  //@dump-sem-ir-end
-  return b;
-}
-
-// CHECK:STDOUT: --- local.carbon
-// CHECK:STDOUT:
-// CHECK:STDOUT: constants {
-// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [concrete]
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
-// CHECK:STDOUT: fn @F() -> out %return.param: %empty_tuple.type {
-// CHECK:STDOUT: !entry:
-// CHECK:STDOUT:   <elided>
-// CHECK:STDOUT:   %a.ref: ref %empty_tuple.type = name_ref a, %a
-// CHECK:STDOUT:   %b: ref %empty_tuple.type = alias_binding b, %a
-// CHECK:STDOUT:   <elided>
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
diff --git a/toolchain/check/testdata/alias/var.carbon b/toolchain/check/testdata/alias/var.carbon
new file mode 100644
index 000000000000..57c02add37eb
--- /dev/null
+++ b/toolchain/check/testdata/alias/var.carbon
@@ -0,0 +1,77 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+// INCLUDE-FILE: toolchain/testing/testdata/min_prelude/destroy.carbon
+//
+// AUTOUPDATE
+// TIP: To test this file alone, run:
+// TIP:   bazel test //toolchain/testing:file_test --test_arg=--file_tests=toolchain/check/testdata/alias/var.carbon
+// TIP: To dump output, run:
+// TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/check/testdata/alias/var.carbon
+
+// --- global.carbon
+
+library "[[@TEST_NAME]]";
+
+var a: () = ();
+
+fn F() -> () {
+  //@dump-sem-ir-begin
+  // TODO: Decide if this should be allowed, and if so, whether it should be
+  // spelled as
+  //
+  //   alias b = ref a;
+  alias b = a;
+  //@dump-sem-ir-end
+  return b;
+}
+
+// --- fail_local.carbon
+
+library "[[@TEST_NAME]]";
+
+fn F() -> () {
+  var a: () = ();
+  //@dump-sem-ir-begin
+  // CHECK:STDERR: fail_local.carbon:[[@LINE+4]]:13: error: alias refers to a runtime value [AliasRequiresConstantValue]
+  // CHECK:STDERR:   alias b = a;
+  // CHECK:STDERR:             ^
+  // CHECK:STDERR:
+  alias b = a;
+  //@dump-sem-ir-end
+  return b;
+}
+
+// CHECK:STDOUT: --- global.carbon
+// CHECK:STDOUT:
+// CHECK:STDOUT: constants {
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [concrete]
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: fn @F() -> out %return.param: %empty_tuple.type {
+// CHECK:STDOUT: !entry:
+// CHECK:STDOUT:   %a.ref: ref %empty_tuple.type = name_ref a, file.%a [concrete = file.%a.var]
+// CHECK:STDOUT:   %b: ref %empty_tuple.type = alias_binding b, %a.ref [concrete = file.%a.var]
+// CHECK:STDOUT:   <elided>
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: fn @__global_init() {
+// CHECK:STDOUT: !entry:
+// CHECK:STDOUT:   <elided>
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: --- fail_local.carbon
+// CHECK:STDOUT:
+// CHECK:STDOUT: constants {
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [concrete]
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: fn @F() -> out %return.param: %empty_tuple.type {
+// CHECK:STDOUT: !entry:
+// CHECK:STDOUT:   <elided>
+// CHECK:STDOUT:   %a.ref: ref %empty_tuple.type = name_ref a, %a
+// CHECK:STDOUT:   %b: ref %empty_tuple.type = alias_binding b, %a.ref
+// CHECK:STDOUT:   <elided>
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/implicit_import.carbon b/toolchain/check/testdata/class/implicit_import.carbon
index 47a18d34b49a..a97616e0a447 100644
--- a/toolchain/check/testdata/class/implicit_import.carbon
+++ b/toolchain/check/testdata/class/implicit_import.carbon
@@ -252,7 +252,7 @@ class B {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %B: type = alias_binding B, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %B: type = alias_binding B, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C;
diff --git a/toolchain/check/testdata/class/import_indirect.carbon b/toolchain/check/testdata/class/import_indirect.carbon
index dc81e17a51e3..486d9eb13d3e 100644
--- a/toolchain/check/testdata/class/import_indirect.carbon
+++ b/toolchain/check/testdata/class/import_indirect.carbon
@@ -188,7 +188,7 @@ var ptr: E* = &value;
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %default.import = import <none>
 // CHECK:STDOUT:   %C.ref.loc6: type = name_ref C, imports.%Main.C [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, imports.%Main.C [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref.loc6 [concrete = constants.%C]
 // CHECK:STDOUT:   name_binding_decl {
 // CHECK:STDOUT:     %b_val.patt: %pattern_type.7c7 = ref_binding_pattern b_val [concrete]
 // CHECK:STDOUT:     %b_val.var_patt: %pattern_type.7c7 = var_pattern %b_val.patt [concrete]
@@ -284,7 +284,7 @@ var ptr: E* = &value;
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %default.import = import <none>
 // CHECK:STDOUT:   %C.ref.loc6: type = name_ref C, imports.%Main.C [concrete = constants.%C]
-// CHECK:STDOUT:   %E: type = alias_binding E, imports.%Main.C [concrete = constants.%C]
+// CHECK:STDOUT:   %E: type = alias_binding E, %C.ref.loc6 [concrete = constants.%C]
 // CHECK:STDOUT:   name_binding_decl {
 // CHECK:STDOUT:     %c_val.patt: %pattern_type.7c7 = ref_binding_pattern c_val [concrete]
 // CHECK:STDOUT:     %c_val.var_patt: %pattern_type.7c7 = var_pattern %c_val.patt [concrete]
diff --git a/toolchain/check/testdata/class/indirect_import_member.carbon b/toolchain/check/testdata/class/indirect_import_member.carbon
index cb293d1720f5..7f8ce16eb8fb 100644
--- a/toolchain/check/testdata/class/indirect_import_member.carbon
+++ b/toolchain/check/testdata/class/indirect_import_member.carbon
@@ -221,7 +221,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT: class @D {
 // CHECK:STDOUT:   %package.ref: <namespace> = name_ref package, package [concrete = package]
 // CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Main.C [concrete = constants.%C]
-// CHECK:STDOUT:   %C: type = alias_binding C, imports.%Main.C [concrete = constants.%C]
+// CHECK:STDOUT:   %C: type = alias_binding C, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %complete_type: <witness> = complete_type_witness constants.%empty_struct_type [concrete = constants.%complete_type]
 // CHECK:STDOUT:   complete_type_witness = %complete_type
 // CHECK:STDOUT:
@@ -440,7 +440,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT:   %Main.D: type = import_ref Main//e, D, loaded [concrete = constants.%D]
 // CHECK:STDOUT:   %Main.import_ref.8f2: <witness> = import_ref Main//e, loc8_1, loaded [concrete = constants.%complete_type]
 // CHECK:STDOUT:   %Main.import_ref.1d5 = import_ref Main//e, inst{{[0-9A-F]+}} [no loc], unloaded
-// CHECK:STDOUT:   %Main.import_ref.7a9: type = import_ref Main//e, loc7_9, loaded [concrete = constants.%C]
+// CHECK:STDOUT:   %Main.import_ref.c58: type = import_ref Main//e, loc7_9, loaded [concrete = constants.%C]
 // CHECK:STDOUT:   %Main.import_ref.8f3: <witness> = import_ref Main//e, inst{{[0-9A-F]+}} [indirect], loaded [concrete = constants.%complete_type]
 // CHECK:STDOUT:   %Main.import_ref.76e = import_ref Main//e, inst{{[0-9A-F]+}} [indirect], unloaded
 // CHECK:STDOUT:   %Main.import_ref.c63: %C.F.type = import_ref Main//e, inst{{[0-9A-F]+}} [indirect], loaded [concrete = constants.%C.F]
@@ -469,7 +469,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%Main.import_ref.1d5
-// CHECK:STDOUT:   .C = imports.%Main.import_ref.7a9
+// CHECK:STDOUT:   .C = imports.%Main.import_ref.c58
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C [from "e.carbon"] {
@@ -485,7 +485,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT: fn @__global_init() {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %D.ref: type = name_ref D, imports.%Main.D [concrete = constants.%D]
-// CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Main.import_ref.7a9 [concrete = constants.%C]
+// CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Main.import_ref.c58 [concrete = constants.%C]
 // CHECK:STDOUT:   %F.ref: %C.F.type = name_ref F, imports.%Main.import_ref.c63 [concrete = constants.%C.F]
 // CHECK:STDOUT:   %C.F.call: init %empty_tuple.type = call %F.ref()
 // CHECK:STDOUT:   assign file.%x.var, %C.F.call
@@ -510,7 +510,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT:   %Main.D: type = import_ref Main//e, D, loaded [concrete = constants.%D]
 // CHECK:STDOUT:   %Main.import_ref.8f2: <witness> = import_ref Main//e, loc8_1, loaded [concrete = constants.%complete_type]
 // CHECK:STDOUT:   %Main.import_ref.1d5 = import_ref Main//e, inst{{[0-9A-F]+}} [no loc], unloaded
-// CHECK:STDOUT:   %Main.import_ref.7a9: type = import_ref Main//e, loc7_9, loaded [concrete = constants.%C]
+// CHECK:STDOUT:   %Main.import_ref.c58: type = import_ref Main//e, loc7_9, loaded [concrete = constants.%C]
 // CHECK:STDOUT:   %Main.import_ref.8f3: <witness> = import_ref Main//e, inst{{[0-9A-F]+}} [indirect], loaded [concrete = constants.%complete_type]
 // CHECK:STDOUT:   %Main.import_ref.76e = import_ref Main//e, inst{{[0-9A-F]+}} [indirect], unloaded
 // CHECK:STDOUT:   %Main.import_ref.c63: %C.F.type = import_ref Main//e, inst{{[0-9A-F]+}} [indirect], loaded [concrete = constants.%C.F]
@@ -539,7 +539,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%Main.import_ref.1d5
-// CHECK:STDOUT:   .C = imports.%Main.import_ref.7a9
+// CHECK:STDOUT:   .C = imports.%Main.import_ref.c58
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C [from "e.carbon"] {
@@ -555,7 +555,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT: fn @__global_init() {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %D.ref: type = name_ref D, imports.%Main.D [concrete = constants.%D]
-// CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Main.import_ref.7a9 [concrete = constants.%C]
+// CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Main.import_ref.c58 [concrete = constants.%C]
 // CHECK:STDOUT:   %F.ref: %C.F.type = name_ref F, imports.%Main.import_ref.c63 [concrete = constants.%C.F]
 // CHECK:STDOUT:   %C.F.call: init %empty_tuple.type = call %F.ref()
 // CHECK:STDOUT:   assign file.%x.var, %C.F.call
diff --git a/toolchain/check/testdata/class/method/method.carbon b/toolchain/check/testdata/class/method/method.carbon
index b276f36a8081..6ffc79db3e82 100644
--- a/toolchain/check/testdata/class/method/method.carbon
+++ b/toolchain/check/testdata/class/method/method.carbon
@@ -343,7 +343,7 @@ fn CallGOnInitializingExpr() -> i32 {
 // CHECK:STDOUT:     %return: ref %i32 = return_slot %return.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %F.ref: %Class.F.type = name_ref F, %Class.F.decl [concrete = constants.%Class.F]
-// CHECK:STDOUT:   %A: %Class.F.type = alias_binding A, %Class.F.decl [concrete = constants.%Class.F]
+// CHECK:STDOUT:   %A: %Class.F.type = alias_binding A, %F.ref [concrete = constants.%Class.F]
 // CHECK:STDOUT:   %i32: type = type_literal constants.%i32 [concrete = constants.%i32]
 // CHECK:STDOUT:   %.loc21: %Class.elem = field_decl k, element0 [concrete]
 // CHECK:STDOUT:   %complete_type: <witness> = complete_type_witness constants.%struct_type.k.0bf [concrete = constants.%complete_type.954]
diff --git a/toolchain/check/testdata/class/syntactic_merge.carbon b/toolchain/check/testdata/class/syntactic_merge.carbon
index 2c398b4c3743..9716a84760e8 100644
--- a/toolchain/check/testdata/class/syntactic_merge.carbon
+++ b/toolchain/check/testdata/class/syntactic_merge.carbon
@@ -211,7 +211,7 @@ fn Base.F[ref self: Base]() {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type = class_decl @Foo [concrete = constants.%Foo.generic] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -532,7 +532,7 @@ fn Base.F[ref self: Base]() {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl: %Foo.type = class_decl @Foo [concrete = constants.%Foo.generic] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -706,7 +706,7 @@ fn Base.F[ref self: Base]() {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.337be0.1 = class_decl @Foo.loc7 [concrete = constants.%Foo.generic.6e878d.1] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -788,7 +788,7 @@ fn Base.F[ref self: Base]() {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.337be0.1 = class_decl @Foo.loc7 [concrete = constants.%Foo.generic.6e878d.1] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -870,7 +870,7 @@ fn Base.F[ref self: Base]() {
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.337be0.1 = class_decl @Foo.loc7 [concrete = constants.%Foo.generic.6e878d.1] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -1007,7 +1007,7 @@ fn Base.F[ref self: Base]() {
 // CHECK:STDOUT:   %default.import.loc2_30.1 = import <none>
 // CHECK:STDOUT:   %default.import.loc2_30.2 = import <none>
 // CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Main.C [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, imports.%Main.C [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl: %Foo.type = class_decl @Foo [concrete = constants.%Foo.generic] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
diff --git a/toolchain/check/testdata/function/call/alias.carbon b/toolchain/check/testdata/function/call/alias.carbon
index fd735782de8f..c8e3a1ec773b 100644
--- a/toolchain/check/testdata/function/call/alias.carbon
+++ b/toolchain/check/testdata/function/call/alias.carbon
@@ -64,7 +64,7 @@ fn Main() {
 // CHECK:STDOUT:     %return: ref %empty_tuple.type = return_slot %return.param
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %A.ref: %A.type = name_ref A, %A.decl [concrete = constants.%A]
-// CHECK:STDOUT:   %B: %A.type = alias_binding B, %A.decl [concrete = constants.%A]
+// CHECK:STDOUT:   %B: %A.type = alias_binding B, %A.ref [concrete = constants.%A]
 // CHECK:STDOUT:   %Main.decl: %Main.type = fn_decl @Main [concrete = constants.%Main] {} {}
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/function/definition/implicit_import.carbon b/toolchain/check/testdata/function/definition/implicit_import.carbon
index 2f90bdf5535d..93b3acaa85a6 100644
--- a/toolchain/check/testdata/function/definition/implicit_import.carbon
+++ b/toolchain/check/testdata/function/definition/implicit_import.carbon
@@ -335,7 +335,7 @@ fn B() {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %A.decl: %A.type = fn_decl @A [concrete = constants.%A] {} {}
 // CHECK:STDOUT:   %A.ref: %A.type = name_ref A, %A.decl [concrete = constants.%A]
-// CHECK:STDOUT:   %B: %A.type = alias_binding B, %A.decl [concrete = constants.%A]
+// CHECK:STDOUT:   %B: %A.type = alias_binding B, %A.ref [concrete = constants.%A]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @A();
diff --git a/toolchain/check/testdata/function/definition/syntactic_merge.carbon b/toolchain/check/testdata/function/definition/syntactic_merge.carbon
index 222932447633..2ad2292be647 100644
--- a/toolchain/check/testdata/function/definition/syntactic_merge.carbon
+++ b/toolchain/check/testdata/function/definition/syntactic_merge.carbon
@@ -220,7 +220,7 @@ fn Foo(unused a: const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type = fn_decl @Foo [concrete = constants.%Foo] {
 // CHECK:STDOUT:     %a.param_patt: %pattern_type = value_param_pattern [concrete]
 // CHECK:STDOUT:     %a.patt: %pattern_type = at_binding_pattern a, %a.param_patt [concrete]
@@ -480,7 +480,7 @@ fn Foo(unused a: const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl: %Foo.type = fn_decl @Foo [concrete = constants.%Foo] {
 // CHECK:STDOUT:     %a.param_patt: %pattern_type = value_param_pattern [concrete]
 // CHECK:STDOUT:     %a.patt: %pattern_type = at_binding_pattern a, %a.param_patt [concrete]
@@ -596,7 +596,7 @@ fn Foo(unused a: const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.47530a.1 = fn_decl @Foo.loc7 [concrete = constants.%Foo.9ec12f.1] {
 // CHECK:STDOUT:     %a.param_patt: %pattern_type = value_param_pattern [concrete]
 // CHECK:STDOUT:     %a.patt: %pattern_type = at_binding_pattern a, %a.param_patt [concrete]
@@ -651,7 +651,7 @@ fn Foo(unused a: const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.47530a.1 = fn_decl @Foo.loc7 [concrete = constants.%Foo.9ec12f.1] {
 // CHECK:STDOUT:     %a.param_patt: %pattern_type = value_param_pattern [concrete]
 // CHECK:STDOUT:     %a.patt: %pattern_type = at_binding_pattern a, %a.param_patt [concrete]
@@ -710,7 +710,7 @@ fn Foo(unused a: const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.47530a.1 = fn_decl @Foo.loc7 [concrete = constants.%Foo.9ec12f.1] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -788,7 +788,7 @@ fn Foo(unused a: const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type = fn_decl @Foo [concrete = constants.%Foo] {
 // CHECK:STDOUT:     %return.param_patt: %pattern_type = out_param_pattern [concrete]
 // CHECK:STDOUT:     %return.patt: %pattern_type = return_slot_pattern %return.param_patt, %D.ref [concrete]
@@ -888,7 +888,7 @@ fn Foo(unused a: const (const C)) {}
 // CHECK:STDOUT:   %default.import.loc2_30.1 = import <none>
 // CHECK:STDOUT:   %default.import.loc2_30.2 = import <none>
 // CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Main.C [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, imports.%Main.C [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl: %Foo.type = fn_decl @Foo [concrete = constants.%Foo] {
 // CHECK:STDOUT:     %a.param_patt: %pattern_type = value_param_pattern [concrete]
 // CHECK:STDOUT:     %a.patt: %pattern_type = at_binding_pattern a, %a.param_patt [concrete]
diff --git a/toolchain/check/testdata/impl/fail_alias.carbon b/toolchain/check/testdata/impl/fail_alias.carbon
index 023d5eb6495c..b7f2e0de4b87 100644
--- a/toolchain/check/testdata/impl/fail_alias.carbon
+++ b/toolchain/check/testdata/impl/fail_alias.carbon
@@ -51,9 +51,9 @@ impl AC as AI {}
 // CHECK:STDOUT:   %I.decl: type = interface_decl @I [concrete = constants.%I.type] {} {}
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %I.ref: type = name_ref I, %I.decl [concrete = constants.%I.type]
-// CHECK:STDOUT:   %AI: type = alias_binding AI, %I.decl [concrete = constants.%I.type]
+// CHECK:STDOUT:   %AI: type = alias_binding AI, %I.ref [concrete = constants.%I.type]
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %AC: type = alias_binding AC, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %AC: type = alias_binding AC, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   impl_decl @C.as.I.impl.e47215.1 [concrete] {} {
 // CHECK:STDOUT:     %AC.ref: type = name_ref AC, file.%AC [concrete = constants.%C]
 // CHECK:STDOUT:     %AI.ref: type = name_ref AI, file.%AI [concrete = constants.%I.type]
diff --git a/toolchain/check/testdata/impl/fail_impl_bad_assoc_fn.carbon b/toolchain/check/testdata/impl/fail_impl_bad_assoc_fn.carbon
index 43fedd3c57ce..3d3c68a88802 100644
--- a/toolchain/check/testdata/impl/fail_impl_bad_assoc_fn.carbon
+++ b/toolchain/check/testdata/impl/fail_impl_bad_assoc_fn.carbon
@@ -599,7 +599,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: impl @FAlias.as.I.impl: %Self.ref as %I.ref {
 // CHECK:STDOUT:   %PossiblyF.ref: %PossiblyF.type = name_ref PossiblyF, file.%PossiblyF.decl [concrete = constants.%PossiblyF]
-// CHECK:STDOUT:   %F: %PossiblyF.type = alias_binding F, file.%PossiblyF.decl [concrete = constants.%PossiblyF]
+// CHECK:STDOUT:   %F: %PossiblyF.type = alias_binding F, %PossiblyF.ref [concrete = constants.%PossiblyF]
 // CHECK:STDOUT:   %I.impl_witness_table = impl_witness_table (<error>), @FAlias.as.I.impl [concrete]
 // CHECK:STDOUT:   %I.impl_witness: <witness> = impl_witness %I.impl_witness_table [concrete = constants.%I.impl_witness.109]
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/lookup/alias.carbon b/toolchain/check/testdata/impl/lookup/alias.carbon
index 54a5a3f367b1..f582f23310e1 100644
--- a/toolchain/check/testdata/impl/lookup/alias.carbon
+++ b/toolchain/check/testdata/impl/lookup/alias.carbon
@@ -105,7 +105,7 @@ fn G(c: C) {
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT:   %HasF.ref: type = name_ref HasF, file.%HasF.decl [concrete = constants.%HasF.type]
 // CHECK:STDOUT:   %F.ref: %HasF.assoc_type = name_ref F, @HasF.WithSelf.%assoc0 [concrete = constants.%assoc0]
-// CHECK:STDOUT:   %G: %HasF.assoc_type = alias_binding G, @HasF.WithSelf.%assoc0 [concrete = constants.%assoc0]
+// CHECK:STDOUT:   %G: %HasF.assoc_type = alias_binding G, %F.ref [concrete = constants.%assoc0]
 // CHECK:STDOUT:   %complete_type: <witness> = complete_type_witness constants.%empty_struct_type [concrete = constants.%complete_type]
 // CHECK:STDOUT:   complete_type_witness = %complete_type
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/lookup/fail_alias_impl_not_found.carbon b/toolchain/check/testdata/impl/lookup/fail_alias_impl_not_found.carbon
index 77ea4ec49c36..3ffb459ac3f2 100644
--- a/toolchain/check/testdata/impl/lookup/fail_alias_impl_not_found.carbon
+++ b/toolchain/check/testdata/impl/lookup/fail_alias_impl_not_found.carbon
@@ -87,7 +87,7 @@ fn F(c: C) {
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT:   %I.ref: type = name_ref I, file.%I.decl [concrete = constants.%I.type]
 // CHECK:STDOUT:   %F.ref: %I.assoc_type = name_ref F, @I.WithSelf.%assoc0 [concrete = constants.%assoc0]
-// CHECK:STDOUT:   %F: %I.assoc_type = alias_binding F, @I.WithSelf.%assoc0 [concrete = constants.%assoc0]
+// CHECK:STDOUT:   %F: %I.assoc_type = alias_binding F, %F.ref [concrete = constants.%assoc0]
 // CHECK:STDOUT:   %complete_type: <witness> = complete_type_witness constants.%empty_struct_type [concrete = constants.%complete_type]
 // CHECK:STDOUT:   complete_type_witness = %complete_type
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interface/fail_assoc_const_alias.carbon b/toolchain/check/testdata/interface/fail_assoc_const_alias.carbon
index 9982b1c4a01a..e3ac262b1597 100644
--- a/toolchain/check/testdata/interface/fail_assoc_const_alias.carbon
+++ b/toolchain/check/testdata/interface/fail_assoc_const_alias.carbon
@@ -105,7 +105,7 @@ interface C {
 // CHECK:STDOUT: !with Self:
 // CHECK:STDOUT:   %I2.ref: type = name_ref I2, file.%I2.decl [concrete = constants.%I2.type]
 // CHECK:STDOUT:   %T2.ref: %I2.assoc_type = name_ref T2, @T2.%assoc0 [concrete = constants.%assoc0.7c1]
-// CHECK:STDOUT:   %U2: %I2.assoc_type = alias_binding U2, @T2.%assoc0 [concrete = constants.%assoc0.7c1]
+// CHECK:STDOUT:   %U2: %I2.assoc_type = alias_binding U2, %T2.ref [concrete = constants.%assoc0.7c1]
 // CHECK:STDOUT:   %J2.WithSelf.F2.decl: @J2.WithSelf.%J2.WithSelf.F2.type (%J2.WithSelf.F2.type) = fn_decl @J2.WithSelf.F2 [symbolic = @J2.WithSelf.%J2.WithSelf.F2 (constants.%J2.WithSelf.F2)] {
 // CHECK:STDOUT:     %return.param_patt: @J2.WithSelf.F2.%pattern_type (%pattern_type.a14) = out_param_pattern [concrete]
 // CHECK:STDOUT:     %return.patt: @J2.WithSelf.F2.%pattern_type (%pattern_type.a14) = return_slot_pattern %return.param_patt, %U2.ref [concrete]
diff --git a/toolchain/check/testdata/interface/import.carbon b/toolchain/check/testdata/interface/import.carbon
index 3ba4655ff8cd..203682598520 100644
--- a/toolchain/check/testdata/interface/import.carbon
+++ b/toolchain/check/testdata/interface/import.carbon
@@ -333,16 +333,16 @@ var f: ForwardDeclared* = &f_ref.f;
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %Basic.ref.loc10: type = name_ref Basic, imports.%Main.Basic [concrete = constants.%Basic.type]
 // CHECK:STDOUT:   %T.ref.loc10: %Basic.assoc_type = name_ref T, imports.%Main.import_ref.736 [concrete = constants.%assoc0.a68]
-// CHECK:STDOUT:   %UseBasicT: %Basic.assoc_type = alias_binding UseBasicT, imports.%Main.import_ref.736 [concrete = constants.%assoc0.a68]
+// CHECK:STDOUT:   %UseBasicT: %Basic.assoc_type = alias_binding UseBasicT, %T.ref.loc10 [concrete = constants.%assoc0.a68]
 // CHECK:STDOUT:   %Basic.ref.loc11: type = name_ref Basic, imports.%Main.Basic [concrete = constants.%Basic.type]
 // CHECK:STDOUT:   %F.ref.loc11: %Basic.assoc_type = name_ref F, imports.%Main.import_ref.c83 [concrete = constants.%assoc1.448]
-// CHECK:STDOUT:   %UseBasicF: %Basic.assoc_type = alias_binding UseBasicF, imports.%Main.import_ref.c83 [concrete = constants.%assoc1.448]
+// CHECK:STDOUT:   %UseBasicF: %Basic.assoc_type = alias_binding UseBasicF, %F.ref.loc11 [concrete = constants.%assoc1.448]
 // CHECK:STDOUT:   %ForwardDeclared.ref.loc13: type = name_ref ForwardDeclared, imports.%Main.ForwardDeclared [concrete = constants.%ForwardDeclared.type]
 // CHECK:STDOUT:   %T.ref.loc13: %ForwardDeclared.assoc_type = name_ref T, imports.%Main.import_ref.fa6 [concrete = constants.%assoc0.c28]
-// CHECK:STDOUT:   %UseForwardDeclaredT: %ForwardDeclared.assoc_type = alias_binding UseForwardDeclaredT, imports.%Main.import_ref.fa6 [concrete = constants.%assoc0.c28]
+// CHECK:STDOUT:   %UseForwardDeclaredT: %ForwardDeclared.assoc_type = alias_binding UseForwardDeclaredT, %T.ref.loc13 [concrete = constants.%assoc0.c28]
 // CHECK:STDOUT:   %ForwardDeclared.ref.loc14: type = name_ref ForwardDeclared, imports.%Main.ForwardDeclared [concrete = constants.%ForwardDeclared.type]
 // CHECK:STDOUT:   %F.ref.loc14: %ForwardDeclared.assoc_type = name_ref F, imports.%Main.import_ref.9f2 [concrete = constants.%assoc1.e73]
-// CHECK:STDOUT:   %UseForwardDeclaredF: %ForwardDeclared.assoc_type = alias_binding UseForwardDeclaredF, imports.%Main.import_ref.9f2 [concrete = constants.%assoc1.e73]
+// CHECK:STDOUT:   %UseForwardDeclaredF: %ForwardDeclared.assoc_type = alias_binding UseForwardDeclaredF, %F.ref.loc14 [concrete = constants.%assoc1.e73]
 // CHECK:STDOUT:   name_binding_decl {
 // CHECK:STDOUT:     %f.patt: %pattern_type.063 = ref_binding_pattern f [concrete]
 // CHECK:STDOUT:     %f.var_patt: %pattern_type.063 = var_pattern %f.patt [concrete]
diff --git a/toolchain/check/testdata/interface/syntactic_merge.carbon b/toolchain/check/testdata/interface/syntactic_merge.carbon
index cfe5fa7c1965..2ec386dee8c2 100644
--- a/toolchain/check/testdata/interface/syntactic_merge.carbon
+++ b/toolchain/check/testdata/interface/syntactic_merge.carbon
@@ -219,7 +219,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.5ed = interface_decl @Foo [concrete = constants.%Foo.generic] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -578,7 +578,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl: %Foo.type = interface_decl @Foo [concrete = constants.%Foo.generic] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -795,7 +795,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.5ede67.1 = interface_decl @Foo.loc7 [concrete = constants.%Foo.generic.fda91f.1] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -885,7 +885,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.5ede67.1 = interface_decl @Foo.loc7 [concrete = constants.%Foo.generic.fda91f.1] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -975,7 +975,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %C.decl: type = class_decl @C [concrete = constants.%C] {} {}
 // CHECK:STDOUT:   %C.ref: type = name_ref C, %C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, %C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl.loc7: %Foo.type.5ede67.1 = interface_decl @Foo.loc7 [concrete = constants.%Foo.generic.fda91f.1] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
@@ -1123,7 +1123,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:   %default.import.loc2_30.1 = import <none>
 // CHECK:STDOUT:   %default.import.loc2_30.2 = import <none>
 // CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Main.C [concrete = constants.%C]
-// CHECK:STDOUT:   %D: type = alias_binding D, imports.%Main.C [concrete = constants.%C]
+// CHECK:STDOUT:   %D: type = alias_binding D, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT:   %Foo.decl: %Foo.type.5ede67.2 = interface_decl @Foo.loc17 [concrete = constants.%Foo.generic.fda91f.2] {
 // CHECK:STDOUT:     %a.patt: %pattern_type = symbolic_binding_pattern a, 0 [concrete]
 // CHECK:STDOUT:   } {
diff --git a/toolchain/check/testdata/interop/cpp/basics/import/cpp_namespace.carbon b/toolchain/check/testdata/interop/cpp/basics/import/cpp_namespace.carbon
index 22f7096fefe1..e67b11aec92c 100644
--- a/toolchain/check/testdata/interop/cpp/basics/import/cpp_namespace.carbon
+++ b/toolchain/check/testdata/interop/cpp/basics/import/cpp_namespace.carbon
@@ -118,7 +118,7 @@ fn F() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: file {
 // CHECK:STDOUT:   %Cpp.ref: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
-// CHECK:STDOUT:   %MyCpp: <namespace> = alias_binding MyCpp, imports.%Cpp [concrete = imports.%Cpp]
+// CHECK:STDOUT:   %MyCpp: <namespace> = alias_binding MyCpp, %Cpp.ref [concrete = imports.%Cpp]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- api_and_impl.carbon
diff --git a/toolchain/check/testdata/interop/cpp/class/export/class.carbon b/toolchain/check/testdata/interop/cpp/class/export/class.carbon
index 5119f61e61e5..ffe6ee17f1c1 100644
--- a/toolchain/check/testdata/interop/cpp/class/export/class.carbon
+++ b/toolchain/check/testdata/interop/cpp/class/export/class.carbon
@@ -84,13 +84,13 @@ class B(N:! i32) {
 
 // TODO: Once we allow this, we should produce an "invalid array bound" error
 // during monomorphization triggered by the C++ code.
-// CHECK:STDERR: fail_todo_monomorphization_failure.carbon:[[@LINE+4]]:11: error: alias initializer must be a name reference [AliasRequiresNameRef]
-// CHECK:STDERR: alias T = B(-1);
-// CHECK:STDERR:           ^~~~~
-// CHECK:STDERR:
 alias T = B(-1);
 
 inline Cpp '''
+// CHECK:STDERR: fail_todo_monomorphization_failure.carbon:[[@LINE+8]]:1: error: semantics TODO: `interop with unsupported type` [SemanticsTodo]
+// CHECK:STDERR: Carbon::T t;
+// CHECK:STDERR: ^
+// CHECK:STDERR:
 // CHECK:STDERR: fail_todo_monomorphization_failure.carbon:[[@LINE+4]]:9: error: no type named 'T' in namespace 'Carbon' [CppInteropParseError]
 // CHECK:STDERR:    22 | Carbon::T t;
 // CHECK:STDERR:       | ~~~~~~~~^
diff --git a/toolchain/check/testdata/namespace/alias.carbon b/toolchain/check/testdata/namespace/alias.carbon
index 8c88378791b4..b8078e1fcaee 100644
--- a/toolchain/check/testdata/namespace/alias.carbon
+++ b/toolchain/check/testdata/namespace/alias.carbon
@@ -85,7 +85,7 @@ fn D() -> i32 { return C(); }
 // CHECK:STDOUT:     .A = %A.decl
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %NS.ref.loc17: <namespace> = name_ref NS, %NS [concrete = %NS]
-// CHECK:STDOUT:   %ns: <namespace> = alias_binding ns, %NS [concrete = %NS]
+// CHECK:STDOUT:   %ns: <namespace> = alias_binding ns, %NS.ref.loc17 [concrete = %NS]
 // CHECK:STDOUT:   %A.decl: %A.type = fn_decl @A [concrete = constants.%A] {
 // CHECK:STDOUT:     %return.param_patt: %pattern_type.7ce = out_param_pattern [concrete]
 // CHECK:STDOUT:     %return.patt: %pattern_type.7ce = return_slot_pattern %return.param_patt, %i32 [concrete]
@@ -106,7 +106,7 @@ fn D() -> i32 { return C(); }
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %NS.ref.loc23: <namespace> = name_ref NS, %NS [concrete = %NS]
 // CHECK:STDOUT:   %A.ref: %A.type = name_ref A, %A.decl [concrete = constants.%A]
-// CHECK:STDOUT:   %C: %A.type = alias_binding C, %A.decl [concrete = constants.%A]
+// CHECK:STDOUT:   %C: %A.type = alias_binding C, %A.ref [concrete = constants.%A]
 // CHECK:STDOUT:   %D.decl: %D.type = fn_decl @D [concrete = constants.%D] {
 // CHECK:STDOUT:     %return.param_patt: %pattern_type.7ce = out_param_pattern [concrete]
 // CHECK:STDOUT:     %return.patt: %pattern_type.7ce = return_slot_pattern %return.param_patt, %i32 [concrete]
diff --git a/toolchain/check/testdata/namespace/fail_decl_in_alias.carbon b/toolchain/check/testdata/namespace/fail_decl_in_alias.carbon
index 40d82a324d25..5e11e7f21f7e 100644
--- a/toolchain/check/testdata/namespace/fail_decl_in_alias.carbon
+++ b/toolchain/check/testdata/namespace/fail_decl_in_alias.carbon
@@ -78,7 +78,7 @@ fn ns.A() -> i32 { return 0; }
 // CHECK:STDOUT:   %Core.import = import Core
 // CHECK:STDOUT:   %NS: <namespace> = namespace [concrete] {}
 // CHECK:STDOUT:   %NS.ref: <namespace> = name_ref NS, %NS [concrete = %NS]
-// CHECK:STDOUT:   %ns: <namespace> = alias_binding ns, %NS [concrete = %NS]
+// CHECK:STDOUT:   %ns: <namespace> = alias_binding ns, %NS.ref [concrete = %NS]
 // CHECK:STDOUT:   %A.decl: %A.type = fn_decl @A [concrete = constants.%A] {
 // CHECK:STDOUT:     %return.param_patt: %pattern_type.7ce = out_param_pattern [concrete]
 // CHECK:STDOUT:     %return.patt: %pattern_type.7ce = return_slot_pattern %return.param_patt, %i32 [concrete]
diff --git a/toolchain/check/testdata/packages/cross_package_export.carbon b/toolchain/check/testdata/packages/cross_package_export.carbon
index f270fa6df657..582f8cbad07e 100644
--- a/toolchain/check/testdata/packages/cross_package_export.carbon
+++ b/toolchain/check/testdata/packages/cross_package_export.carbon
@@ -905,7 +905,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %Other.import = import Other
 // CHECK:STDOUT:   %Other.ref: <namespace> = name_ref Other, imports.%Other [concrete = imports.%Other]
 // CHECK:STDOUT:   %C.ref: %C.type = name_ref C, imports.%Other.C [concrete = constants.%C]
-// CHECK:STDOUT:   %C: %C.type = alias_binding C, imports.%Other.C [concrete = constants.%C]
+// CHECK:STDOUT:   %C: %C.type = alias_binding C, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @C [from "conflict.carbon"];
@@ -939,7 +939,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %Other.import = import Other
 // CHECK:STDOUT:   %Other.ref: <namespace> = name_ref Other, imports.%Other [concrete = imports.%Other]
 // CHECK:STDOUT:   %C.ref: type = name_ref C, imports.%Other.C [concrete = constants.%C]
-// CHECK:STDOUT:   %C: type = alias_binding C, imports.%Other.C [concrete = constants.%C]
+// CHECK:STDOUT:   %C: type = alias_binding C, %C.ref [concrete = constants.%C]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C [from "export_name.carbon"] {
diff --git a/toolchain/check/testdata/packages/export_import.carbon b/toolchain/check/testdata/packages/export_import.carbon
index e5aed17db6ce..f228c93c02eb 100644
--- a/toolchain/check/testdata/packages/export_import.carbon
+++ b/toolchain/check/testdata/packages/export_import.carbon
@@ -767,7 +767,7 @@ export Poison;
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %default.import = import <none>
 // CHECK:STDOUT:   %C.ref: <error> = name_ref C, <error> [concrete = <error>]
-// CHECK:STDOUT:   %Local: <error> = alias_binding Local, <error> [concrete = <error>]
+// CHECK:STDOUT:   %Local: <error> = alias_binding Local, %C.ref [concrete = <error>]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- use_non_export_then_base.carbon
diff --git a/toolchain/check/testdata/packages/export_name.carbon b/toolchain/check/testdata/packages/export_name.carbon
index c0d8397952c0..8f97867bedd1 100644
--- a/toolchain/check/testdata/packages/export_name.carbon
+++ b/toolchain/check/testdata/packages/export_name.carbon
@@ -988,10 +988,10 @@ private export C;
 // CHECK:STDOUT:   }
 // CHECK:STDOUT:   %default.import = import <none>
 // CHECK:STDOUT:   %C.ref: <error> = name_ref C, <error> [concrete = <error>]
-// CHECK:STDOUT:   %Local: <error> = alias_binding Local, <error> [concrete = <error>]
+// CHECK:STDOUT:   %Local: <error> = alias_binding Local, %C.ref [concrete = <error>]
 // CHECK:STDOUT:   %NS.ref: <error> = name_ref NS, <error> [concrete = <error>]
 // CHECK:STDOUT:   %NSC.ref: <error> = name_ref NSC, <error> [concrete = <error>]
-// CHECK:STDOUT:   %NSLocal: <error> = alias_binding NSLocal, <error> [concrete = <error>]
+// CHECK:STDOUT:   %NSLocal: <error> = alias_binding NSLocal, %NSC.ref [concrete = <error>]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- repeat_export.carbon
diff --git a/toolchain/diagnostics/kind.def b/toolchain/diagnostics/kind.def
index f227971de3a3..26d8399b1a33 100644
--- a/toolchain/diagnostics/kind.def
+++ b/toolchain/diagnostics/kind.def
@@ -547,7 +547,7 @@ CARBON_DIAGNOSTIC_KIND(ClassMemberDeclaration)
 CARBON_DIAGNOSTIC_KIND(ClassInvalidMemberAccess)
 
 // Alias diagnostics.
-CARBON_DIAGNOSTIC_KIND(AliasRequiresNameRef)
+CARBON_DIAGNOSTIC_KIND(AliasRequiresConstantValue)
 
 // Where operator and its requirements.
 CARBON_DIAGNOSTIC_KIND(ImplsOnNonFacetType)
diff --git a/toolchain/lower/testdata/alias/local.carbon b/toolchain/lower/testdata/alias/local.carbon
deleted file mode 100644
index fc0f689d5909..000000000000
--- a/toolchain/lower/testdata/alias/local.carbon
+++ /dev/null
@@ -1,64 +0,0 @@
-// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
-// Exceptions. See /LICENSE for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-// INCLUDE-FILE: toolchain/testing/testdata/min_prelude/int.carbon
-//
-// AUTOUPDATE
-// TIP: To test this file alone, run:
-// TIP:   bazel test //toolchain/testing:file_test --test_arg=--file_tests=toolchain/lower/testdata/alias/local.carbon
-// TIP: To dump output, run:
-// TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/lower/testdata/alias/local.carbon
-
-fn F() -> i32 {
-  var a: i32 = 0;
-  alias b = a;
-  return b;
-}
-
-// CHECK:STDOUT: ; ModuleID = 'local.carbon'
-// CHECK:STDOUT: source_filename = "local.carbon"
-// CHECK:STDOUT:
-// CHECK:STDOUT: ; Function Attrs: nounwind
-// CHECK:STDOUT: define i32 @_CF.Main() #0 !dbg !4 {
-// CHECK:STDOUT: entry:
-// CHECK:STDOUT:   %a.var = alloca i32, align 4, !dbg !8
-// CHECK:STDOUT:   call void @llvm.lifetime.start.p0(ptr %a.var), !dbg !8
-// CHECK:STDOUT:   store i32 0, ptr %a.var, align 4, !dbg !8
-// CHECK:STDOUT:   %.loc16 = load i32, ptr %a.var, align 4, !dbg !9
-// CHECK:STDOUT:   call void @"_COp.7e389eab4a7e5487:core.Destroy.Core"(ptr %a.var), !dbg !8
-// CHECK:STDOUT:   ret i32 %.loc16, !dbg !10
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
-// CHECK:STDOUT: ; Function Attrs: nounwind
-// CHECK:STDOUT: define weak_odr void @"_COp.7e389eab4a7e5487:core.Destroy.Core"(ptr %self) #0 !dbg !11 {
-// CHECK:STDOUT: entry:
-// CHECK:STDOUT:   ret void, !dbg !16
-// CHECK:STDOUT: }
-// CHECK:STDOUT:
-// CHECK:STDOUT: ; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
-// CHECK:STDOUT: declare void @llvm.lifetime.start.p0(ptr captures(none)) #1
-// CHECK:STDOUT:
-// CHECK:STDOUT: attributes #0 = { nounwind }
-// CHECK:STDOUT: attributes #1 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
-// CHECK:STDOUT:
-// CHECK:STDOUT: !llvm.module.flags = !{!0, !1}
-// CHECK:STDOUT: !llvm.dbg.cu = !{!2}
-// CHECK:STDOUT:
-// CHECK:STDOUT: !0 = !{i32 7, !"Dwarf Version", i32 5}
-// CHECK:STDOUT: !1 = !{i32 2, !"Debug Info Version", i32 3}
-// CHECK:STDOUT: !2 = distinct !DICompileUnit(language: DW_LANG_C_plus_plus, file: !3, producer: "carbon", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug)
-// CHECK:STDOUT: !3 = !DIFile(filename: "local.carbon", directory: "")
-// CHECK:STDOUT: !4 = distinct !DISubprogram(name: "F", linkageName: "_CF.Main", scope: null, file: !3, line: 13, type: !5, spFlags: DISPFlagDefinition, unit: !2)
-// CHECK:STDOUT: !5 = !DISubroutineType(types: !6)
-// CHECK:STDOUT: !6 = !{!7}
-// CHECK:STDOUT: !7 = !DIBasicType(name: "int", size: 32, encoding: DW_ATE_signed)
-// CHECK:STDOUT: !8 = !DILocation(line: 14, column: 3, scope: !4)
-// CHECK:STDOUT: !9 = !DILocation(line: 16, column: 10, scope: !4)
-// CHECK:STDOUT: !10 = !DILocation(line: 16, column: 3, scope: !4)
-// CHECK:STDOUT: !11 = distinct !DISubprogram(name: "Op", linkageName: "_COp.7e389eab4a7e5487:core.Destroy.Core", scope: null, file: !3, line: 14, type: !12, spFlags: DISPFlagDefinition, unit: !2, retainedNodes: !14)
-// CHECK:STDOUT: !12 = !DISubroutineType(types: !13)
-// CHECK:STDOUT: !13 = !{null, !7}
-// CHECK:STDOUT: !14 = !{!15}
-// CHECK:STDOUT: !15 = !DILocalVariable(arg: 1, scope: !11, type: !7)
-// CHECK:STDOUT: !16 = !DILocation(line: 14, column: 3, scope: !11)
diff --git a/toolchain/lower/testdata/alias/var.carbon b/toolchain/lower/testdata/alias/var.carbon
new file mode 100644
index 000000000000..263ffad6bc1f
--- /dev/null
+++ b/toolchain/lower/testdata/alias/var.carbon
@@ -0,0 +1,59 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+// INCLUDE-FILE: toolchain/testing/testdata/min_prelude/int.carbon
+//
+// AUTOUPDATE
+// TIP: To test this file alone, run:
+// TIP:   bazel test //toolchain/testing:file_test --test_arg=--file_tests=toolchain/lower/testdata/alias/var.carbon
+// TIP: To dump output, run:
+// TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/lower/testdata/alias/var.carbon
+
+var a: i32 = 0;
+
+fn F() -> i32 {
+  alias b = a;
+  return b;
+}
+
+// CHECK:STDOUT: ; ModuleID = 'var.carbon'
+// CHECK:STDOUT: source_filename = "var.carbon"
+// CHECK:STDOUT:
+// CHECK:STDOUT: @_Ca.Main = global i32 0
+// CHECK:STDOUT: @llvm.global_ctors = appending global [1 x { i32, ptr, ptr }] [{ i32, ptr, ptr } { i32 0, ptr @_C__global_init.Main, ptr null }]
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: nounwind
+// CHECK:STDOUT: define i32 @_CF.Main() #0 !dbg !4 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %.loc17 = load i32, ptr @_Ca.Main, align 4, !dbg !8
+// CHECK:STDOUT:   ret i32 %.loc17, !dbg !9
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: nounwind
+// CHECK:STDOUT: define internal void @_C__global_init.Main() #0 !dbg !10 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   store i32 0, ptr @_Ca.Main, align 4, !dbg !13
+// CHECK:STDOUT:   ret void, !dbg !14
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: attributes #0 = { nounwind }
+// CHECK:STDOUT:
+// CHECK:STDOUT: !llvm.module.flags = !{!0, !1}
+// CHECK:STDOUT: !llvm.dbg.cu = !{!2}
+// CHECK:STDOUT:
+// CHECK:STDOUT: !0 = !{i32 7, !"Dwarf Version", i32 5}
+// CHECK:STDOUT: !1 = !{i32 2, !"Debug Info Version", i32 3}
+// CHECK:STDOUT: !2 = distinct !DICompileUnit(language: DW_LANG_C_plus_plus, file: !3, producer: "carbon", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug)
+// CHECK:STDOUT: !3 = !DIFile(filename: "var.carbon", directory: "")
+// CHECK:STDOUT: !4 = distinct !DISubprogram(name: "F", linkageName: "_CF.Main", scope: null, file: !3, line: 15, type: !5, spFlags: DISPFlagDefinition, unit: !2)
+// CHECK:STDOUT: !5 = !DISubroutineType(types: !6)
+// CHECK:STDOUT: !6 = !{!7}
+// CHECK:STDOUT: !7 = !DIBasicType(name: "int", size: 32, encoding: DW_ATE_signed)
+// CHECK:STDOUT: !8 = !DILocation(line: 17, column: 10, scope: !4)
+// CHECK:STDOUT: !9 = !DILocation(line: 17, column: 3, scope: !4)
+// CHECK:STDOUT: !10 = distinct !DISubprogram(name: "__global_init", linkageName: "_C__global_init.Main", scope: null, file: !3, type: !11, spFlags: DISPFlagDefinition, unit: !2)
+// CHECK:STDOUT: !11 = !DISubroutineType(types: !12)
+// CHECK:STDOUT: !12 = !{null}
+// CHECK:STDOUT: !13 = !DILocation(line: 13, column: 1, scope: !10)
+// CHECK:STDOUT: !14 = !DILocation(line: 0, scope: !10)