diff --git a/clang/include/clang/Basic/Module.h b/clang/include/clang/Basic/Module.h
--- a/clang/include/clang/Basic/Module.h
+++ b/clang/include/clang/Basic/Module.h
@@ -141,6 +141,9 @@
   /// The name of the umbrella entry, as written in the module map.
   std::string UmbrellaAsWritten;
 
+  // The path to the umbrella entry relative to the root module's \c Directory.
+  std::string UmbrellaRelativeToRootModuleDirectory;
+
   /// The module through which entities defined in this module will
   /// eventually be exposed, for use in "private" modules.
   std::string ExportAsModule;
@@ -188,6 +191,7 @@
   /// file.
   struct Header {
     std::string NameAsWritten;
+    std::string PathRelativeToRootModuleDirectory;
     const FileEntry *Entry;
 
     explicit operator bool() { return Entry; }
@@ -197,6 +201,7 @@
   /// file.
   struct DirectoryName {
     std::string NameAsWritten;
+    std::string PathRelativeToRootModuleDirectory;
     const DirectoryEntry *Entry;
 
     explicit operator bool() { return Entry; }
@@ -545,7 +550,8 @@
   /// module.
   Header getUmbrellaHeader() const {
     if (auto *FE = Umbrella.dyn_cast<const FileEntry *>())
-      return Header{UmbrellaAsWritten, FE};
+      return Header{UmbrellaAsWritten, UmbrellaRelativeToRootModuleDirectory,
+                    FE};
     return Header{};
   }
 
diff --git a/clang/include/clang/Lex/ModuleMap.h b/clang/include/clang/Lex/ModuleMap.h
--- a/clang/include/clang/Lex/ModuleMap.h
+++ b/clang/include/clang/Lex/ModuleMap.h
@@ -649,12 +649,14 @@
   /// Sets the umbrella header of the given module to the given
   /// header.
   void setUmbrellaHeader(Module *Mod, const FileEntry *UmbrellaHeader,
-                         Twine NameAsWritten);
+                         const Twine &NameAsWritten,
+                         const Twine &PathRelativeToRootModuleDirectory);
 
   /// Sets the umbrella directory of the given module to the given
   /// directory.
   void setUmbrellaDir(Module *Mod, const DirectoryEntry *UmbrellaDir,
-                      Twine NameAsWritten);
+                      const Twine &NameAsWritten,
+                      const Twine &PathRelativeToRootModuleDirectory);
 
   /// Adds this header to the given module.
   /// \param Role The role of the header wrt the module.
diff --git a/clang/lib/Basic/Module.cpp b/clang/lib/Basic/Module.cpp
--- a/clang/lib/Basic/Module.cpp
+++ b/clang/lib/Basic/Module.cpp
@@ -245,9 +245,10 @@
 
 Module::DirectoryName Module::getUmbrellaDir() const {
   if (Header U = getUmbrellaHeader())
-    return {"", U.Entry->getDir()};
+    return {"", "", U.Entry->getDir()};
 
-  return {UmbrellaAsWritten, Umbrella.dyn_cast<const DirectoryEntry *>()};
+  return {UmbrellaAsWritten, UmbrellaRelativeToRootModuleDirectory,
+          Umbrella.dyn_cast<const DirectoryEntry *>()};
 }
 
 void Module::addTopHeader(const FileEntry *File) {
diff --git a/clang/lib/Frontend/FrontendAction.cpp b/clang/lib/Frontend/FrontendAction.cpp
--- a/clang/lib/Frontend/FrontendAction.cpp
+++ b/clang/lib/Frontend/FrontendAction.cpp
@@ -342,7 +342,8 @@
       // file relative to the module build directory (the directory containing
       // the module map file) so this will find the same file that we found
       // while parsing the module map.
-      addHeaderInclude(H.NameAsWritten, Includes, LangOpts, Module->IsExternC);
+      addHeaderInclude(H.PathRelativeToRootModuleDirectory, Includes, LangOpts,
+                       Module->IsExternC);
     }
   }
   // Note that Module->PrivateHeaders will not be a TopHeader.
@@ -351,8 +352,8 @@
     Module->addTopHeader(UmbrellaHeader.Entry);
     if (Module->Parent)
       // Include the umbrella header for submodules.
-      addHeaderInclude(UmbrellaHeader.NameAsWritten, Includes, LangOpts,
-                       Module->IsExternC);
+      addHeaderInclude(UmbrellaHeader.PathRelativeToRootModuleDirectory,
+                       Includes, LangOpts, Module->IsExternC);
   } else if (Module::DirectoryName UmbrellaDir = Module->getUmbrellaDir()) {
     // Add all of the headers we find in this subdirectory.
     std::error_code EC;
@@ -386,7 +387,8 @@
       auto PathIt = llvm::sys::path::rbegin(Dir->path());
       for (int I = 0; I != Dir.level() + 1; ++I, ++PathIt)
         Components.push_back(*PathIt);
-      SmallString<128> RelativeHeader(UmbrellaDir.NameAsWritten);
+      SmallString<128> RelativeHeader(
+          UmbrellaDir.PathRelativeToRootModuleDirectory);
       for (auto It = Components.rbegin(), End = Components.rend(); It != End;
            ++It)
         llvm::sys::path::append(RelativeHeader, *It);
@@ -470,7 +472,7 @@
   // Dig out the module definition.
   HeaderSearch &HS = CI.getPreprocessor().getHeaderSearchInfo();
   Module *M = HS.lookupModule(CI.getLangOpts().CurrentModule,
-                              /*AllowSearch=*/false);
+                              /*AllowSearch=*/true);
   if (!M) {
     CI.getDiagnostics().Report(diag::err_missing_module)
       << CI.getLangOpts().CurrentModule << ModuleMapFilename;
@@ -528,8 +530,8 @@
   SmallString<256> HeaderContents;
   std::error_code Err = std::error_code();
   if (Module::Header UmbrellaHeader = M->getUmbrellaHeader())
-    addHeaderInclude(UmbrellaHeader.NameAsWritten, HeaderContents,
-                     CI.getLangOpts(), M->IsExternC);
+    addHeaderInclude(UmbrellaHeader.PathRelativeToRootModuleDirectory,
+                     HeaderContents, CI.getLangOpts(), M->IsExternC);
   Err = collectModuleHeaderIncludes(
       CI.getLangOpts(), FileMgr, CI.getDiagnostics(),
       CI.getPreprocessor().getHeaderSearchInfo().getModuleMap(), M,
diff --git a/clang/lib/Frontend/FrontendActions.cpp b/clang/lib/Frontend/FrontendActions.cpp
--- a/clang/lib/Frontend/FrontendActions.cpp
+++ b/clang/lib/Frontend/FrontendActions.cpp
@@ -297,7 +297,8 @@
         << Name;
       continue;
     }
-    Headers.push_back({std::string(Name), &FE->getFileEntry()});
+    Headers.push_back(
+        {std::string(Name), std::string(Name), &FE->getFileEntry()});
   }
   HS.getModuleMap().createHeaderModule(CI.getLangOpts().CurrentModule, Headers);
 
diff --git a/clang/lib/Lex/ModuleMap.cpp b/clang/lib/Lex/ModuleMap.cpp
--- a/clang/lib/Lex/ModuleMap.cpp
+++ b/clang/lib/Lex/ModuleMap.cpp
@@ -260,9 +260,10 @@
           << UmbrellaMod->getFullModuleName();
       else
         // Record this umbrella header.
-        setUmbrellaHeader(Mod, *File, RelativePathName.str());
+        setUmbrellaHeader(Mod, *File, Header.FileName, RelativePathName.str());
     } else {
-      Module::Header H = {std::string(RelativePathName.str()), *File};
+      Module::Header H = {Header.FileName, std::string(RelativePathName.str()),
+                          *File};
       if (Header.Kind == Module::HK_Excluded)
         excludeHeader(Mod, H);
       else
@@ -305,7 +306,7 @@
     return false;
 
   auto Role = headerKindToRole(Header.Kind);
-  Module::Header H = {std::string(Path.str()), *File};
+  Module::Header H = {Header.FileName, std::string(Path.str()), *File};
   addHeader(Mod, H, Role);
   return true;
 }
@@ -1038,11 +1039,13 @@
   Result->NoUndeclaredIncludes |= Attrs.NoUndeclaredIncludes;
   Result->Directory = FrameworkDir;
 
+  // Chop off the first framework bit, as that is implied.
+  StringRef RelativePath = UmbrellaName.str().substr(
+      Result->getTopLevelModule()->Directory->getName().size());
+  RelativePath = llvm::sys::path::relative_path(RelativePath);
+
   // umbrella header "umbrella-header-name"
-  //
-  // The "Headers/" component of the name is implied because this is
-  // a framework module.
-  setUmbrellaHeader(Result, *UmbrellaHeader, ModuleName + ".h");
+  setUmbrellaHeader(Result, *UmbrellaHeader, ModuleName + ".h", RelativePath);
 
   // export *
   Result->Exports.push_back(Module::ExportDecl(nullptr, true));
@@ -1121,11 +1124,14 @@
   return Result;
 }
 
-void ModuleMap::setUmbrellaHeader(Module *Mod, const FileEntry *UmbrellaHeader,
-                                  Twine NameAsWritten) {
+void ModuleMap::setUmbrellaHeader(
+    Module *Mod, const FileEntry *UmbrellaHeader, const Twine &NameAsWritten,
+    const Twine &PathRelativeToRootModuleDirectory) {
   Headers[UmbrellaHeader].push_back(KnownHeader(Mod, NormalHeader));
   Mod->Umbrella = UmbrellaHeader;
   Mod->UmbrellaAsWritten = NameAsWritten.str();
+  Mod->UmbrellaRelativeToRootModuleDirectory =
+      PathRelativeToRootModuleDirectory.str();
   UmbrellaDirs[UmbrellaHeader->getDir()] = Mod;
 
   // Notify callbacks that we just added a new header.
@@ -1134,9 +1140,12 @@
 }
 
 void ModuleMap::setUmbrellaDir(Module *Mod, const DirectoryEntry *UmbrellaDir,
-                               Twine NameAsWritten) {
+                               const Twine &NameAsWritten,
+                               const Twine &PathRelativeToRootModuleDirectory) {
   Mod->Umbrella = UmbrellaDir;
   Mod->UmbrellaAsWritten = NameAsWritten.str();
+  Mod->UmbrellaRelativeToRootModuleDirectory =
+      PathRelativeToRootModuleDirectory.str();
   UmbrellaDirs[UmbrellaDir] = Mod;
 }
 
@@ -2405,6 +2414,7 @@
   }
 
   std::string DirName = std::string(Tok.getString());
+  std::string DirNameAsWritten = DirName;
   SourceLocation DirNameLoc = consumeToken();
 
   // Check whether we already have an umbrella.
@@ -2446,7 +2456,7 @@
     for (llvm::vfs::recursive_directory_iterator I(FS, Dir->getName(), EC), E;
          I != E && !EC; I.increment(EC)) {
       if (auto FE = SourceMgr.getFileManager().getFile(I->path())) {
-        Module::Header Header = {std::string(I->path()), *FE};
+        Module::Header Header = {"", std::string(I->path()), *FE};
         Headers.push_back(std::move(Header));
       }
     }
@@ -2467,7 +2477,7 @@
   }
 
   // Record this umbrella directory.
-  Map.setUmbrellaDir(ActiveModule, Dir, DirName);
+  Map.setUmbrellaDir(ActiveModule, Dir, DirNameAsWritten, DirName);
 }
 
 /// Parse a module export declaration.
diff --git a/clang/lib/Serialization/ASTReader.cpp b/clang/lib/Serialization/ASTReader.cpp
--- a/clang/lib/Serialization/ASTReader.cpp
+++ b/clang/lib/Serialization/ASTReader.cpp
@@ -1921,10 +1921,9 @@
     std::string Filename = std::string(key.Filename);
     if (key.Imported)
       Reader.ResolveImportedPath(M, Filename);
-    // FIXME: This is not always the right filename-as-written, but we're not
-    // going to use this information to rebuild the module, so it doesn't make
-    // a lot of difference.
-    Module::Header H = {std::string(key.Filename), *FileMgr.getFile(Filename)};
+    // FIXME: NameAsWritten
+    Module::Header H = {std::string(key.Filename), "",
+                        *FileMgr.getFile(Filename)};
     ModMap.addHeader(Mod, H, HeaderRole, /*Imported*/true);
     HFI.isModuleHeader |= !(HeaderRole & ModuleMap::TextualHeader);
   }
@@ -5618,7 +5617,8 @@
       ResolveImportedPath(F, Filename);
       if (auto Umbrella = PP.getFileManager().getFile(Filename)) {
         if (!CurrentModule->getUmbrellaHeader())
-          ModMap.setUmbrellaHeader(CurrentModule, *Umbrella, Blob);
+          // FIXME: NameAsWritten
+          ModMap.setUmbrellaHeader(CurrentModule, *Umbrella, Blob, "");
         else if (CurrentModule->getUmbrellaHeader().Entry != *Umbrella) {
           if ((ClientLoadCapabilities & ARR_OutOfDate) == 0)
             Error("mismatched umbrella headers in submodule");
@@ -5651,7 +5651,8 @@
       ResolveImportedPath(F, Dirname);
       if (auto Umbrella = PP.getFileManager().getDirectory(Dirname)) {
         if (!CurrentModule->getUmbrellaDir())
-          ModMap.setUmbrellaDir(CurrentModule, *Umbrella, Blob);
+          // FIXME: NameAsWritten
+          ModMap.setUmbrellaDir(CurrentModule, *Umbrella, Blob, "");
         else if (CurrentModule->getUmbrellaDir().Entry != *Umbrella) {
           if ((ClientLoadCapabilities & ARR_OutOfDate) == 0)
             Error("mismatched umbrella directories in submodule");
diff --git a/clang/test/Modules/Inputs/explicit-build-inferred/frameworks/Inferred.framework/Headers/Inferred.h b/clang/test/Modules/Inputs/explicit-build-inferred/frameworks/Inferred.framework/Headers/Inferred.h
new file mode 100644
--- /dev/null
+++ b/clang/test/Modules/Inputs/explicit-build-inferred/frameworks/Inferred.framework/Headers/Inferred.h
@@ -0,0 +1 @@
+typedef int inferred;
diff --git a/clang/test/Modules/Inputs/explicit-build-inferred/frameworks/module.modulemap b/clang/test/Modules/Inputs/explicit-build-inferred/frameworks/module.modulemap
new file mode 100644
--- /dev/null
+++ b/clang/test/Modules/Inputs/explicit-build-inferred/frameworks/module.modulemap
@@ -0,0 +1 @@
+framework module * {}
diff --git a/clang/test/Modules/explicit-build-inferred.cpp b/clang/test/Modules/explicit-build-inferred.cpp
new file mode 100644
--- /dev/null
+++ b/clang/test/Modules/explicit-build-inferred.cpp
@@ -0,0 +1,13 @@
+// RUN: rm -rf %t && mkdir %t
+//
+// RUN: %clang_cc1 -fmodules -fno-implicit-modules -fimplicit-module-maps \
+// RUN:   -emit-module -x c++ %S/Inputs/explicit-build-inferred/frameworks/module.modulemap \
+// RUN:   -fmodule-name=Inferred -o %t/Inferred.pcm -F %S/Inputs/explicit-build-inferred/frameworks
+//
+// RUN: %clang_cc1 -fmodules -fno-implicit-modules -fsyntax-only %s \
+// RUN:   -fmodule-map-file=%S/Inputs/explicit-build-inferred/frameworks/module.modulemap \
+// RUN:   -fmodule-file=%t/Inferred.pcm -F %S/Inputs/explicit-build-inferred/frameworks
+
+#include <Inferred/Inferred.h>
+
+inferred a = 0;