diff --git a/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.h b/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.h
--- a/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.h
+++ b/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.h
@@ -386,8 +386,10 @@
   /// Return the buffer (memref) for a given OpOperand (tensor). Allocate
   /// a new buffer and copy over data from the existing buffer if out-of-place
   /// bufferization was decided.
-  FailureOr<Value> getBuffer(RewriterBase &rewriter, OpOperand &opOperand,
-                             bool forceInPlace = false) const;
+  FailureOr<Value>
+  getBuffer(RewriterBase &rewriter, OpOperand &opOperand,
+            bool forceInPlace = false,
+            Optional<Operation *> customCopyInsertionPoint = None) const;
 
   /// Return dialect-specific bufferization state.
   template <typename StateT>
diff --git a/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.cpp b/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.cpp
--- a/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.cpp
+++ b/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/BufferizableOpInterface.cpp
@@ -377,7 +377,8 @@
 /// bufferization is necessary.
 FailureOr<Value>
 mlir::linalg::comprehensive_bufferize::BufferizationState::getBuffer(
-    RewriterBase &rewriter, OpOperand &opOperand, bool forceInPlace) const {
+    RewriterBase &rewriter, OpOperand &opOperand, bool forceInPlace,
+    Optional<Operation *> customCopyInsertionPoint) const {
   OpBuilder::InsertionGuard guard(rewriter);
   Operation *op = opOperand.getOwner();
   Location loc = op->getLoc();
@@ -418,9 +419,14 @@
   if (bufferizesToMemoryWrite(opOperand) && !bufferizesToMemoryRead(opOperand))
     return resultBuffer;
 
-  // The copy happens right before the op that is bufferized.
-  rewriter.setInsertionPoint(op);
+  if (customCopyInsertionPoint) {
+    rewriter.setInsertionPoint(*customCopyInsertionPoint);
+  } else {
+    // The copy happens right before the op that is bufferized.
+    rewriter.setInsertionPoint(op);
+  }
   createMemCpy(rewriter, loc, operandBuffer, *resultBuffer);
+
   return resultBuffer;
 }