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
@@ -51,7 +51,8 @@
   let assemblyFormat = "$source attr-dict `:` type($source) `to` type($result)";
 }
 
-def SparseTensor_ConvertOp : SparseTensor_Op<"convert", [SameOperandsAndResultType]>,
+def SparseTensor_ConvertOp : SparseTensor_Op<"convert",
+  [NoSideEffect, SameOperandsAndResultType]>,
     Arguments<(ins AnyTensor:$source)>,
     Results<(outs AnyTensor:$dest)> {
   string summary = "Converts between different tensor types";
@@ -81,6 +82,7 @@
 
   }];
   let assemblyFormat = "$source attr-dict `:` type($source) `to` type($dest)";
+  let hasFolder = 1;
 }
 
 def SparseTensor_ToPointersOp : SparseTensor_Op<"pointers", [NoSideEffect]>,
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
@@ -230,6 +230,12 @@
   return op.emitError("unexpected type in convert");
 }
 
+OpFoldResult ConvertOp::fold(ArrayRef<Attribute> operands) {
+  if (getType() == source().getType())
+    return source();
+  return {};
+}
+
 static LogicalResult verify(ToPointersOp op) {
   if (auto e = getSparseTensorEncoding(op.tensor().getType())) {
     if (failed(isInBounds(op.dim(), op.tensor())))
diff --git a/mlir/test/Dialect/SparseTensor/conversion.mlir b/mlir/test/Dialect/SparseTensor/conversion.mlir
--- a/mlir/test/Dialect/SparseTensor/conversion.mlir
+++ b/mlir/test/Dialect/SparseTensor/conversion.mlir
@@ -112,6 +112,14 @@
   return %0 : tensor<?x?x?xf32, #SparseTensor>
 }
 
+// CHECK-LABEL: func @sparse_nop_convert(
+//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>) -> !llvm.ptr<i8>
+//       CHECK: return %[[A]] : !llvm.ptr<i8>
+func @sparse_nop_convert(%arg0: tensor<64xf32, #SparseVector>) -> tensor<64xf32, #SparseVector> {
+  %0 = sparse_tensor.convert %arg0 : tensor<64xf32, #SparseVector> to tensor<64xf32, #SparseVector>
+  return %0 : tensor<64xf32, #SparseVector>
+}
+
 // CHECK-LABEL: func @sparse_convert_1d(
 //  CHECK-SAME: %[[A:.*]]: tensor<?xi32>) -> !llvm.ptr<i8>
 //   CHECK-DAG: %[[C0:.*]] = constant 0 : index
diff --git a/mlir/test/Dialect/SparseTensor/fold.mlir b/mlir/test/Dialect/SparseTensor/fold.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Dialect/SparseTensor/fold.mlir
@@ -0,0 +1,20 @@
+// RUN: mlir-opt %s  --canonicalize --cse | FileCheck %s
+
+#SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
+
+// CHECK-LABEL: func @sparse_nop_convert(
+//  CHECK-SAME: %[[A:.*]]: tensor<64xf32, #{{.*}}>)
+//       CHECK: return %[[A]] : tensor<64xf32, #{{.*}}>
+func @sparse_nop_convert(%arg0: tensor<64xf32, #SparseVector>) -> tensor<64xf32, #SparseVector> {
+  %0 = sparse_tensor.convert %arg0 : tensor<64xf32, #SparseVector> to tensor<64xf32, #SparseVector>
+  return %0 : tensor<64xf32, #SparseVector>
+}
+
+// CHECK-LABEL: func @sparse_dce_convert(
+//  CHECK-SAME: %[[A:.*]]: tensor<64xf32>)
+//   CHECK-NOT: sparse_tensor.convert
+//       CHECK: return
+func @sparse_dce_convert(%arg0: tensor<64xf32>) {
+  %0 = sparse_tensor.convert %arg0 : tensor<64xf32> to tensor<64xf32, #SparseVector>
+  return
+}