diff --git a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
--- a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
+++ b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
@@ -86,6 +86,7 @@
 
   }];
   let assemblyFormat = "$source attr-dict `:` type($source) `to` type($dest)";
+  let hasFolder = 1;
   let hasVerifier = 1;
 }
 
diff --git a/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp b/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
--- a/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
+++ b/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
@@ -333,6 +333,17 @@
   return emitError("unexpected type in convert");
 }
 
+OpFoldResult ConvertOp::fold(ArrayRef<Attribute> operands) {
+  Type dstType = getType();
+  // Fold trivial dense-to-dense convert and leave trivial sparse-to-sparse
+  // convert for codegen to remove. This is because we use trivial
+  // sparse-to-sparse to tell bufferization that the sparse codegen will expand
+  // the tensor buffer into sparse tensor storage.
+  if (!getSparseTensorEncoding(dstType) && dstType == getSource().getType())
+    return getSource();
+  return {};
+}
+
 LogicalResult ToPointersOp::verify() {
   auto e = getSparseTensorEncoding(getTensor().getType());
   if (failed(isInBounds(getDimension().getZExtValue(), getTensor())))
diff --git a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorCodegen.cpp b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorCodegen.cpp
--- a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorCodegen.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorCodegen.cpp
@@ -727,7 +727,10 @@
   LogicalResult
   matchAndRewrite(ConvertOp op, OpAdaptor adaptor,
                   ConversionPatternRewriter &rewriter) const override {
-    if (op.getType() != op.getSource().getType()) {
+    SparseTensorEncodingAttr encDst = getSparseTensorEncoding(op.getType());
+    SparseTensorEncodingAttr encSrc =
+        getSparseTensorEncoding(op.getSource().getType());
+    if (encDst != encSrc) {
       // This should be handled by rewriting before codegen.
       return failure();
     }
diff --git a/mlir/test/Dialect/SparseTensor/codegen.mlir b/mlir/test/Dialect/SparseTensor/codegen.mlir
--- a/mlir/test/Dialect/SparseTensor/codegen.mlir
+++ b/mlir/test/Dialect/SparseTensor/codegen.mlir
@@ -526,7 +526,7 @@
 //  CHECK-SAME:   %[[A3:.*]]: memref<?xi64>,
 //  CHECK-SAME:   %[[A4:.*]]: memref<?xf32>)
 //       CHECK:   return %[[A0]], %[[A1]], %[[A2]], %[[A3]], %[[A4]] : memref<1xindex>, memref<3xindex>, memref<?xi32>, memref<?xi64>, memref<?xf32>
-func.func @sparse_nop_convert(%arg0: tensor<?xf32, #SparseVector>) -> tensor<?xf32, #SparseVector> {
-  %0 = sparse_tensor.convert %arg0 : tensor<?xf32, #SparseVector> to tensor<?xf32, #SparseVector>
+func.func @sparse_nop_convert(%arg0: tensor<32xf32, #SparseVector>) -> tensor<?xf32, #SparseVector> {
+  %0 = sparse_tensor.convert %arg0 : tensor<32xf32, #SparseVector> to tensor<?xf32, #SparseVector>
   return %0 : tensor<?xf32, #SparseVector>
 }
diff --git a/mlir/test/Dialect/SparseTensor/fold.mlir b/mlir/test/Dialect/SparseTensor/fold.mlir
--- a/mlir/test/Dialect/SparseTensor/fold.mlir
+++ b/mlir/test/Dialect/SparseTensor/fold.mlir
@@ -2,6 +2,15 @@
 
 #SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
 
+// CHECK-LABEL: func @sparse_nop_dense2dense_convert(
+//  CHECK-SAME: %[[A:.*]]: tensor<64xf32>)
+//   CHECK-NOT: sparse_tensor.convert
+//       CHECK: return %[[A]] : tensor<64xf32>
+func.func @sparse_nop_dense2dense_convert(%arg0: tensor<64xf32>) -> tensor<64xf32> {
+  %0 = sparse_tensor.convert %arg0 : tensor<64xf32> to tensor<64xf32>
+  return %0 : tensor<64xf32>
+}
+
 // CHECK-LABEL: func @sparse_dce_convert(
 //  CHECK-SAME: %[[A:.*]]: tensor<64xf32>)
 //   CHECK-NOT: sparse_tensor.convert