diff --git a/llvm/lib/Linker/IRMover.cpp b/llvm/lib/Linker/IRMover.cpp
--- a/llvm/lib/Linker/IRMover.cpp
+++ b/llvm/lib/Linker/IRMover.cpp
@@ -242,15 +242,6 @@
   bool IsUniqued = !isa<StructType>(Ty) || cast<StructType>(Ty)->isLiteral();
 
   if (!IsUniqued) {
-    StructType *STy = cast<StructType>(Ty);
-    // This is actually a type from the destination module, this can be reached
-    // when this type is loaded in another module, added to DstStructTypesSet,
-    // and then we reach the same type in another module where it has not been
-    // added to MappedTypes. (PR37684)
-    if (STy->getContext().isODRUniquingDebugTypes() && !STy->isOpaque() &&
-        DstStructTypesSet.hasType(STy))
-      return *Entry = STy;
-
 #ifndef NDEBUG
     for (auto &Pair : MappedTypes) {
       assert(!(Pair.first != Ty && Pair.second == Ty) &&
@@ -258,7 +249,7 @@
     }
 #endif
 
-    if (!Visited.insert(STy).second) {
+    if (!Visited.insert(cast<StructType>(Ty)).second) {
       StructType *DTy = StructType::create(Ty->getContext());
       return *Entry = DTy;
     }
@@ -579,6 +570,13 @@
   if (!SGV)
     return nullptr;
 
+  // When linking a global from other modules than source & dest, skip
+  // materializing it because it would be mapped later when its containing
+  // module is linked. Linking it now would potentially pull in many types that
+  // may not be mapped properly.
+  if (SGV->getParent() != &DstM && SGV->getParent() != SrcM.get())
+    return nullptr;
+
   Expected<Constant *> NewProto = linkGlobalValueProto(SGV, ForIndirectSymbol);
   if (!NewProto) {
     setError(NewProto.takeError());
diff --git a/llvm/test/LTO/X86/Inputs/type-mapping-bug4.ll b/llvm/test/LTO/X86/Inputs/type-mapping-bug4.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/LTO/X86/Inputs/type-mapping-bug4.ll
@@ -0,0 +1,25 @@
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+%"T2" = type opaque
+%"T3" = type { i32 }
+
+define i32 @a(%"T2"*) !dbg !6 {
+  %X = alloca %"T3"
+  %W = getelementptr %"T3", %"T3"* %X, i32 0, i32 0
+  %V = load i32, i32* %W
+  ret i32 %V
+}
+
+!llvm.module.flags = !{!0, !1}
+!llvm.dbg.cu = !{!2}
+!0 = !{i32 1, !"ThinLTO", i32 0}
+!1 = !{i32 2, !"Debug Info Version", i32 3}
+!2 = distinct !DICompileUnit(language: DW_LANG_C_plus_plus, file: !3, retainedTypes: !4)
+!3 = !DIFile(filename: "f2", directory: "")
+!4 = !{!5}
+
+; This DICompositeType refers to !5 in type-mapping-bug4.ll
+!5 = !DICompositeType(tag: DW_TAG_structure_type, flags: DIFlagFwdDecl, identifier: "SHARED")
+
+!6 = distinct !DISubprogram(unit: !2)
diff --git a/llvm/test/LTO/X86/type-mapping-bug4.ll b/llvm/test/LTO/X86/type-mapping-bug4.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/LTO/X86/type-mapping-bug4.ll
@@ -0,0 +1,36 @@
+; RUN: opt -module-summary -o %t0.o %S/Inputs/type-mapping-bug4.ll
+; RUN: opt -module-summary -o %t1.o %s
+; RUN: llvm-lto2 run -o %t2 --save-temps %t0.o %t1.o -r %t0.o,a,px -r %t1.o,a, -r %t1.o,c,px
+; RUN: llvm-dis < %t2.0.0.preopt.bc | FileCheck %s
+
+; CHECK: %T2 = type { i32 }
+; makes sure %T3 was not renamed %T3.0 because the linking of C is skipped.
+; CHECK: %T3 = type { i32 }
+
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+%"T2" = type { i32 }
+%"T3" = type { i32 }
+
+define void @c(%"T3"*) {
+  ret void
+}
+
+declare void @a(%"T2"*)
+
+!llvm.dbg.cu = !{!2}
+!llvm.module.flags = !{!0, !1}
+!0 = !{i32 1, !"ThinLTO", i32 0}
+!1 = !{i32 2, !"Debug Info Version", i32 3}
+!2 = distinct !DICompileUnit(language: DW_LANG_C_plus_plus, file: !3, retainedTypes: !4)
+!3 = !DIFile(filename: "f1", directory: "")
+!4 = !{!5}
+
+; This DICompositeType is referenced by !5 in Inputs/type-mapping-bug4.ll
+; causing the function type in !7 to be added to its module.
+!5 = !DICompositeType(tag: DW_TAG_structure_type, templateParams: !6, identifier: "SHARED")
+!6 = !{!7}
+
+; The reference to d and T3 that gets loaded into %t0.o
+!7 = !DITemplateValueParameter(value: void (%"T3"*)* @c)