diff --git a/llvm/lib/Analysis/InstructionSimplify.cpp b/llvm/lib/Analysis/InstructionSimplify.cpp
--- a/llvm/lib/Analysis/InstructionSimplify.cpp
+++ b/llvm/lib/Analysis/InstructionSimplify.cpp
@@ -5819,6 +5819,74 @@
   return ::SimplifyFreezeInst(Op0, Q);
 }
 
+static Constant *ConstructLoadOperandConstant(Value *Op) {
+  SmallVector<Value *, 4> Worklist;
+  Worklist.push_back(Op);
+  while (true) {
+    Value *CurOp = Worklist.back();
+    if (isa<Constant>(CurOp))
+      break;
+    if (auto *BC = dyn_cast<BitCastOperator>(CurOp)) {
+      Worklist.push_back(BC->getOperand(0));
+    } else if (auto *GEP = dyn_cast<GEPOperator>(CurOp)) {
+      for (unsigned I = 1; I != GEP->getNumOperands(); ++I) {
+        if (!isa<Constant>(GEP->getOperand(I)))
+          return nullptr;
+      }
+      Worklist.push_back(GEP->getOperand(0));
+    } else if (auto *II = dyn_cast<IntrinsicInst>(CurOp)) {
+      if (II->isLaunderOrStripInvariantGroup())
+        Worklist.push_back(II->getOperand(0));
+      else
+        return nullptr;
+    } else {
+      return nullptr;
+    }
+  }
+
+  Constant *NewOp = cast<Constant>(Worklist.pop_back_val());
+  while (!Worklist.empty()) {
+    Value *CurOp = Worklist.pop_back_val();
+    if (isa<BitCastOperator>(CurOp)) {
+      NewOp = ConstantExpr::getBitCast(NewOp, CurOp->getType());
+    } else if (auto *GEP = dyn_cast<GEPOperator>(CurOp)) {
+      SmallVector<Constant *> Idxs;
+      Idxs.reserve(GEP->getNumOperands() - 1);
+      for (unsigned I = 1, E = GEP->getNumOperands(); I != E; ++I) {
+        Idxs.push_back(cast<Constant>(GEP->getOperand(I)));
+      }
+      NewOp = ConstantExpr::getGetElementPtr(GEP->getSourceElementType(), NewOp,
+                                             Idxs, GEP->isInBounds(),
+                                             GEP->getInRangeIndex());
+    } else {
+      assert(isa<IntrinsicInst>(CurOp) &&
+             cast<IntrinsicInst>(CurOp)->isLaunderOrStripInvariantGroup() &&
+             "expected invariant group intrinsic");
+      NewOp = ConstantExpr::getBitCast(NewOp, CurOp->getType());
+    }
+  }
+  return NewOp;
+}
+
+static Value *SimplifyLoadInst(LoadInst *LI, const SimplifyQuery &Q) {
+  if (LI->isVolatile())
+    return nullptr;
+
+  if (auto *C = ConstantFoldInstruction(LI, Q.DL))
+    return C;
+
+  // The following only catches more cases than ConstantFoldInstruction() if the
+  // load operand wasn't a constant. Specifically, invariant.group intrinsics.
+  if (isa<Constant>(LI->getPointerOperand()))
+    return nullptr;
+
+  if (auto *C = dyn_cast_or_null<Constant>(
+          ConstructLoadOperandConstant(LI->getPointerOperand())))
+    return ConstantFoldLoadFromConstPtr(C, LI->getType(), Q.DL);
+
+  return nullptr;
+}
+
 /// See if we can compute a simplified version of this instruction.
 /// If not, this returns null.
 
@@ -5975,6 +6043,9 @@
     // No simplifications for Alloca and it can't be constant folded.
     Result = nullptr;
     break;
+  case Instruction::Load:
+    Result = SimplifyLoadInst(cast<LoadInst>(I), Q);
+    break;
   }
 
   /// If called on unreachable code, the above logic may report that the
diff --git a/llvm/test/Transforms/InstSimplify/invariant.group-load.ll b/llvm/test/Transforms/InstSimplify/invariant.group-load.ll
--- a/llvm/test/Transforms/InstSimplify/invariant.group-load.ll
+++ b/llvm/test/Transforms/InstSimplify/invariant.group-load.ll
@@ -9,11 +9,7 @@
 
 define i64 @f() {
 ; CHECK-LABEL: @f(
-; CHECK-NEXT:    [[A:%.*]] = call i8* @llvm.strip.invariant.group.p0i8(i8* bitcast ({ i64, i64 }* @A to i8*))
-; CHECK-NEXT:    [[B:%.*]] = getelementptr i8, i8* [[A]], i32 8
-; CHECK-NEXT:    [[C:%.*]] = bitcast i8* [[B]] to i64*
-; CHECK-NEXT:    [[D:%.*]] = load i64, i64* [[C]], align 4
-; CHECK-NEXT:    ret i64 [[D]]
+; CHECK-NEXT:    ret i64 3
 ;
   %p = bitcast { i64, i64 }* @A to i8*
   %a = call i8* @llvm.strip.invariant.group.p0i8(i8* %p)
@@ -25,11 +21,7 @@
 
 define i64 @g() {
 ; CHECK-LABEL: @g(
-; CHECK-NEXT:    [[A:%.*]] = call i8* @llvm.launder.invariant.group.p0i8(i8* bitcast ({ i64, i64 }* @A to i8*))
-; CHECK-NEXT:    [[B:%.*]] = getelementptr i8, i8* [[A]], i32 8
-; CHECK-NEXT:    [[C:%.*]] = bitcast i8* [[B]] to i64*
-; CHECK-NEXT:    [[D:%.*]] = load i64, i64* [[C]], align 4
-; CHECK-NEXT:    ret i64 [[D]]
+; CHECK-NEXT:    ret i64 3
 ;
   %p = bitcast { i64, i64 }* @A to i8*
   %a = call i8* @llvm.launder.invariant.group.p0i8(i8* %p)