diff --git a/mlir/lib/Dialect/Linalg/Transforms/DropUnitDims.cpp b/mlir/lib/Dialect/Linalg/Transforms/DropUnitDims.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/DropUnitDims.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/DropUnitDims.cpp
@@ -251,7 +251,7 @@
 };
 
 struct UnitExtentReplacementInfo {
-  RankedTensorType type;
+  ShapedType type;
   AffineMap indexMap;
   ArrayAttr reassociation;
 };
@@ -267,8 +267,8 @@
 /// - modified index map that can be used to access the replaced result/operand
 /// - the reassociation that converts from the original tensor type to the
 ///   modified tensor type.
-static UnitExtentReplacementInfo replaceUnitExtents(AffineMap indexMap,
-                                                    RankedTensorType type,
+template <typename T>
+static UnitExtentReplacementInfo replaceUnitExtents(AffineMap indexMap, T type,
                                                     MLIRContext *context) {
   ArrayRef<int64_t> shape = type.getShape();
   ArrayRef<AffineExpr> exprs = indexMap.getResults();
@@ -301,11 +301,11 @@
     reassociations.clear();
     ++dim;
   }
-  UnitExtentReplacementInfo info = {
-      RankedTensorType::get(newShape, type.getElementType()),
-      AffineMap::get(indexMap.getNumDims(), indexMap.getNumSymbols(),
-                     newIndexExprs, context),
-      ArrayAttr::get(context, reassociationMaps)};
+  UnitExtentReplacementInfo info = {T::get(newShape, type.getElementType()),
+                                    AffineMap::get(indexMap.getNumDims(),
+                                                   indexMap.getNumSymbols(),
+                                                   newIndexExprs, context),
+                                    ArrayAttr::get(context, reassociationMaps)};
   return info;
 }
 
@@ -320,14 +320,12 @@
   return reassociationExprs;
 }
 
-/// Pattern to replace tensors operands/results that are unit extents.
-struct ReplaceUnitExtentTensors : public OpRewritePattern<GenericOp> {
+/// Pattern to replace tensor/buffer operands/results that are unit extents.
+template <typename OperandType, typename ReshapeOp>
+struct ReplaceUnitExtents : public OpRewritePattern<GenericOp> {
   using OpRewritePattern<GenericOp>::OpRewritePattern;
   LogicalResult matchAndRewrite(GenericOp genericOp,
                                 PatternRewriter &rewriter) const override {
-    if (!genericOp.hasTensorSemantics())
-      return failure();
-
     MLIRContext *context = rewriter.getContext();
     Location loc = genericOp.getLoc();
 
@@ -337,9 +335,12 @@
     bool doCanonicalization = false;
     for (auto it : llvm::zip(genericOp.getIndexingMaps(),
                              genericOp.getShapedOperandTypes())) {
-      auto replacementInfo = replaceUnitExtents(
-          std::get<0>(it), std::get<1>(it).template cast<RankedTensorType>(),
-          context);
+      auto operand = std::get<1>(it).template dyn_cast<OperandType>();
+      if (!operand)
+        return failure();
+
+      auto replacementInfo =
+          replaceUnitExtents(std::get<0>(it), operand, context);
       reassociationMaps.push_back(replacementInfo.reassociation);
       newIndexingMaps.push_back(replacementInfo.indexMap);
       newInputOutputTypes.push_back(replacementInfo.type);
@@ -363,7 +364,7 @@
         if (operand.value().getType() == newInputOutputTypes[flattenedIdx])
           res.push_back(operand.value());
         else
-          res.push_back(rewriter.create<linalg::TensorReshapeOp>(
+          res.push_back(rewriter.create<ReshapeOp>(
               loc, newInputOutputTypes[flattenedIdx], operand.value(),
               convertAffineMapArrayToExprs(reassociationMaps[flattenedIdx])));
         ++flattenedIdx;
@@ -392,11 +393,11 @@
     SmallVector<Value, 4> resultReplacements;
     for (auto result : llvm::enumerate(replacementOp.getResults())) {
       unsigned index = result.index() + replacementOp.getNumInputs();
-      RankedTensorType origResultType = genericOp.getResult(result.index())
-                                            .getType()
-                                            .template cast<RankedTensorType>();
+      auto origResultType = genericOp.getResult(result.index())
+                                .getType()
+                                .template cast<OperandType>();
       if (origResultType != result.value().getType())
-        resultReplacements.push_back(rewriter.create<linalg::TensorReshapeOp>(
+        resultReplacements.push_back(rewriter.create<ReshapeOp>(
             loc, origResultType, result.value(),
             convertAffineMapArrayToExprs(reassociationMaps[index])));
       else
@@ -497,9 +498,10 @@
 void mlir::linalg::populateFoldUnitExtentDimsPatterns(
     RewritePatternSet &patterns) {
   auto *context = patterns.getContext();
-  patterns.add<FoldUnitDimLoops, ReplaceUnitExtentTensors,
-               UseRankReducedSubTensorOp, UseRankReducedSubTensorInsertOp>(
-      context);
+  patterns
+      .add<FoldUnitDimLoops, ReplaceUnitExtents<MemRefType, linalg::ReshapeOp>,
+           ReplaceUnitExtents<RankedTensorType, linalg::TensorReshapeOp>,
+           UseRankReducedSubTensorOp, UseRankReducedSubTensorInsertOp>(context);
   TensorReshapeOp::getCanonicalizationPatterns(patterns, context);
 }
 
diff --git a/mlir/test/Dialect/Linalg/drop-unit-extent-dims.mlir b/mlir/test/Dialect/Linalg/drop-unit-extent-dims.mlir
--- a/mlir/test/Dialect/Linalg/drop-unit-extent-dims.mlir
+++ b/mlir/test/Dialect/Linalg/drop-unit-extent-dims.mlir
@@ -449,3 +449,40 @@
 //       CHECK:   %[[RESULT:.+]] = subtensor_insert %[[RESHAPE]]
 //  CHECK-SAME:     tensor<f32> into tensor<1x3xf32>
 //       CHECK:   return %[[RESULT]]
+
+// -----
+
+#accesses = [
+  affine_map<(d0, d1) -> (0, 0)>,
+  affine_map<(d0, d1) -> (d0, d1)>
+]
+
+#trait = {
+  indexing_maps = #accesses,
+  iterator_types = ["parallel", "parallel"],
+  library_call = "some_external_fn"
+}
+
+// Confirm the linalg.generic patterns also work on memrefs
+func @broadcast_scalar_memref(%arg0 : memref<1x1xf32>, %shape : memref<?x?xf32>) -> memref<?x?xf32>
+{
+   linalg.generic #trait
+     ins(%arg0 : memref<1x1xf32>)
+    outs(%shape : memref<?x?xf32>) {
+      ^bb0(%arg2 : f32, %arg3 : f32):
+        linalg.yield %arg2 : f32
+   }
+   return %shape : memref<?x?xf32>
+}
+//   CHECK-DAG: #[[$MAP0:.*]] = affine_map<(d0, d1) -> ()>
+//   CHECK-DAG: #[[$MAP1:.*]] = affine_map<(d0, d1) -> (d0, d1)>
+// CHECK-LABEL: func @broadcast_scalar_memref
+//  CHECK-SAME:   %[[ARG0:.*]]: memref<1x1xf32>
+//       CHECK:   %[[A:.*]] = linalg.reshape %[[ARG0]] []
+//  CHECK-SAME:     memref<1x1xf32> into memref<f32>
+//       CHECK:   linalg.generic
+//  CHECK-SAME:     indexing_maps = [#[[$MAP0]], #[[$MAP1]]]
+//  CHECK-SAME:     iterator_types = ["parallel", "parallel"]
+//  CHECK-SAME:     %[[A]]
+
+