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
@@ -155,22 +155,6 @@
   return
 }
 
-// CHECK-LABEL: func @sparse_nop_convert(
-//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>) -> !llvm.ptr<i8>
-//       CHECK: return %[[A]] : !llvm.ptr<i8>
-func.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_hidden_nop_cast(
-//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>) -> !llvm.ptr<i8>
-//       CHECK: return %[[A]] : !llvm.ptr<i8>
-func.func @sparse_hidden_nop_cast(%arg0: tensor<32xf32, #SparseVector>) -> tensor<?xf32, #SparseVector> {
-  %0 = sparse_tensor.convert %arg0 : tensor<32xf32, #SparseVector> to tensor<?xf32, #SparseVector>
-  return %0 : tensor<?xf32, #SparseVector>
-}
-
 // CHECK-LABEL: func @sparse_nop_cast(
 //  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>) -> !llvm.ptr<i8>
 //       CHECK: return %[[A]] : !llvm.ptr<i8>
@@ -179,190 +163,6 @@
   return %0 : tensor<?xf32, #SparseVector>
 }
 
-// CHECK-LABEL: func @sparse_convert_1d(
-//  CHECK-SAME: %[[A:.*]]: tensor<?xi32>) -> !llvm.ptr<i8> {
-//   CHECK-DAG: %[[EmptyCOO:.*]] = arith.constant 4 : i32
-//   CHECK-DAG: %[[FromCOO:.*]] = arith.constant 2 : i32
-//   CHECK-DAG: %[[I0:.*]] = arith.constant 0 : i32
-//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
-//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
-//   CHECK-DAG: %[[U:.*]] = tensor.dim %[[A]], %[[C0]] : tensor<?xi32>
-//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<1xi8>
-//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<1xindex>
-//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<1xindex>
-//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<1xi8> to memref<?xi8>
-//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<1xindex> to memref<?xindex>
-//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<1xindex> to memref<?xindex>
-//       CHECK: %[[NP:.*]] = llvm.mlir.null : !llvm.ptr<i8>
-//       CHECK: %[[C:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[EmptyCOO]], %[[NP]])
-//       CHECK: %[[M:.*]] = memref.alloca() : memref<1xindex>
-//       CHECK: %[[T:.*]] = memref.cast %[[M]] : memref<1xindex> to memref<?xindex>
-//       CHECK: %[[BUF:.*]] = memref.alloca() : memref<i32>
-//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %[[U]] step %[[C1]] {
-//       CHECK:   %[[E:.*]] = tensor.extract %[[A]][%[[I]]] : tensor<?xi32>
-//       CHECK:   %[[N:.*]] = arith.cmpi ne, %[[E]], %[[I0]] : i32
-//       CHECK:   scf.if %[[N]] {
-//       CHECK:     memref.store %[[I]], %[[M]][%[[C0]]] : memref<1xindex>
-//       CHECK:     memref.store %[[E]], %[[BUF]][] : memref<i32>
-//       CHECK:     call @addEltI32(%[[C]], %[[BUF]], %[[T]], %[[Z]])
-//       CHECK:   }
-//       CHECK: }
-//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[FromCOO]], %[[C]])
-//       CHECK: call @delSparseTensorCOOI32(%[[C]])
-//       CHECK: return %[[T]] : !llvm.ptr<i8>
-func.func @sparse_convert_1d(%arg0: tensor<?xi32>) -> tensor<?xi32, #SparseVector> {
-  %0 = sparse_tensor.convert %arg0 : tensor<?xi32> to tensor<?xi32, #SparseVector>
-  return %0 : tensor<?xi32, #SparseVector>
-}
-
-// CHECK-LABEL: func @sparse_convert_complex(
-//  CHECK-SAME: %[[A:.*]]: tensor<100xcomplex<f64>>) -> !llvm.ptr<i8> {
-//   CHECK-DAG: %[[CC:.*]] = complex.constant [0.000000e+00, 0.000000e+00] : complex<f64>
-//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
-//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
-//   CHECK-DAG: %[[C100:.*]] = arith.constant 100 : index
-//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %[[C100]] step %[[C1]] {
-//       CHECK:   %[[E:.*]] = tensor.extract %[[A]][%[[I]]] : tensor<100xcomplex<f64>>
-//       CHECK:   %[[N:.*]] = complex.neq %[[E]], %[[CC]] : complex<f64>
-//       CHECK:   scf.if %[[N]] {
-//       CHECK:     memref.store %[[I]], %{{.*}}[%[[C0]]] : memref<1xindex>
-//       CHECK:     call @addEltC64
-//       CHECK:   }
-//       CHECK: }
-//       CHECK: %[[T:.*]] = call @newSparseTensor
-//       CHECK: call @delSparseTensorCOOC64
-//       CHECK: return %[[T]] : !llvm.ptr<i8>
-func.func @sparse_convert_complex(%arg0: tensor<100xcomplex<f64>>) -> tensor<100xcomplex<f64>, #SparseVector> {
-  %0 = sparse_tensor.convert %arg0 : tensor<100xcomplex<f64>> to tensor<100xcomplex<f64>, #SparseVector>
-  return %0 : tensor<100xcomplex<f64>, #SparseVector>
-}
-
-// CHECK-LABEL: func @sparse_convert_1d_ss(
-//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>)
-//   CHECK-DAG: %[[SparseToSparse:.*]] = arith.constant 3 : i32
-//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<1xi8>
-//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<1xindex>
-//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<1xindex>
-//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<1xi8> to memref<?xi8>
-//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<1xindex> to memref<?xindex>
-//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<1xindex> to memref<?xindex>
-//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[SparseToSparse]], %[[A]])
-//       CHECK: return %[[T]] : !llvm.ptr<i8>
-func.func @sparse_convert_1d_ss(%arg0: tensor<?xf32, #SparseVector64>) -> tensor<?xf32, #SparseVector32> {
-  %0 = sparse_tensor.convert %arg0 : tensor<?xf32, #SparseVector64> to tensor<?xf32, #SparseVector32>
-  return %0 : tensor<?xf32, #SparseVector32>
-}
-
-// CHECK-LABEL: func @sparse_convert_2d(
-//  CHECK-SAME: %[[A:.*]]: tensor<2x4xf64>) -> !llvm.ptr<i8>
-//   CHECK-DAG: %[[EmptyCOO:.*]] = arith.constant 4 : i32
-//   CHECK-DAG: %[[FromCOO:.*]] = arith.constant 2 : i32
-//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
-//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
-//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<2xi8>
-//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<2xindex>
-//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<2xindex>
-//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<2xi8> to memref<?xi8>
-//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<2xindex> to memref<?xindex>
-//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<2xindex> to memref<?xindex>
-//       CHECK: %[[NP:.*]] = llvm.mlir.null : !llvm.ptr<i8>
-//       CHECK: %[[C:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[EmptyCOO]], %[[NP]])
-//       CHECK: %[[M:.*]] = memref.alloca() : memref<2xindex>
-//       CHECK: %[[T:.*]] = memref.cast %[[M]] : memref<2xindex> to memref<?xindex>
-//       CHECK: %[[BUF:.*]] = memref.alloca() : memref<f64>
-//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %{{.*}} step %[[C1]] {
-//       CHECK:   scf.for %[[J:.*]] = %[[C0]] to %{{.*}} step %[[C1]] {
-//       CHECK:     %[[E:.*]] = tensor.extract %[[A]][%[[I]], %[[J]]] : tensor<2x4xf64>
-//       CHECK:     memref.store %[[I]], %[[M]][%[[C0]]] : memref<2xindex>
-//       CHECK:     memref.store %[[J]], %[[M]][%[[C1]]] : memref<2xindex>
-//       CHECK:     memref.store %[[E]], %[[BUF]][] : memref<f64>
-//       CHECK:     call @addEltF64(%[[C]], %[[BUF]], %[[T]], %[[Z]])
-//       CHECK:   }
-//       CHECK: }
-//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[FromCOO]], %[[C]])
-//       CHECK: call @delSparseTensorCOOF64(%[[C]])
-//       CHECK: return %[[T]] : !llvm.ptr<i8>
-func.func @sparse_convert_2d(%arg0: tensor<2x4xf64>) -> tensor<2x4xf64, #CSR> {
-  %0 = sparse_tensor.convert %arg0 : tensor<2x4xf64> to tensor<2x4xf64, #CSR>
-  return %0 : tensor<2x4xf64, #CSR>
-}
-
-// CHECK-LABEL: func @sparse_constant() -> !llvm.ptr<i8> {
-//   CHECK-DAG: %[[EmptyCOO:.*]] = arith.constant 4 : i32
-//   CHECK-DAG: %[[FromCOO:.*]] = arith.constant 2 : i32
-//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
-//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
-//   CHECK-DAG: %[[C2:.*]] = arith.constant 2 : index
-//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<2xi8>
-//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<2xindex>
-//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<2xindex>
-//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<2xi8> to memref<?xi8>
-//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<2xindex> to memref<?xindex>
-//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<2xindex> to memref<?xindex>
-//       CHECK: %[[NP:.*]] = llvm.mlir.null : !llvm.ptr<i8>
-//       CHECK: %[[C:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[EmptyCOO]], %[[NP]])
-//       CHECK: %[[M:.*]] = memref.alloca() : memref<2xindex>
-//       CHECK: %[[N:.*]] = memref.cast %[[M]] : memref<2xindex> to memref<?xindex>
-//       CHECK: %[[BUF:.*]] = memref.alloca() : memref<f32>
-//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %[[C2]] step %[[C1]] {
-//       CHECK:   memref.store %{{.*}}, %[[M]][%[[C0]]] : memref<2xindex>
-//       CHECK:   memref.store %{{.*}}, %[[M]][%[[C1]]] : memref<2xindex>
-//       CHECK:   %[[V:.*]] = tensor.extract %{{.*}}[%[[I]]] : tensor<2xf32>
-//       CHECK:   memref.store %[[V]], %[[BUF]][] : memref<f32>
-//       CHECK:   call @addEltF32(%{{.*}}, %[[BUF]], %[[N]], %{{.*}})
-//       CHECK: }
-//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[FromCOO]], %[[C]])
-//       CHECK: call @delSparseTensorCOOF32(%[[C]])
-//       CHECK: return %[[T]] : !llvm.ptr<i8>
-func.func @sparse_constant() -> tensor<8x7xf32, #CSR>{
-  // Initialize a tensor.
-  %0 = arith.constant sparse<[[0, 0], [1, 6]], [1.0, 5.0]> : tensor<8x7xf32>
-  // Convert the tensor to a sparse tensor.
-  %1 = sparse_tensor.convert %0 : tensor<8x7xf32> to tensor<8x7xf32, #CSR>
-  return %1 : tensor<8x7xf32, #CSR>
-}
-
-// CHECK-LABEL: func @sparse_convert_3d(
-//  CHECK-SAME: %[[A:.*]]: tensor<?x?x?xf64>) -> !llvm.ptr<i8>
-//   CHECK-DAG: %[[EmptyCOO:.*]] = arith.constant 4 : i32
-//   CHECK-DAG: %[[FromCOO:.*]] = arith.constant 2 : i32
-//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
-//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
-//   CHECK-DAG: %[[C2:.*]] = arith.constant 2 : index
-//   CHECK-DAG: %[[U1:.*]] = tensor.dim %[[A]], %[[C0]] : tensor<?x?x?xf64>
-//   CHECK-DAG: %[[U2:.*]] = tensor.dim %[[A]], %[[C1]] : tensor<?x?x?xf64>
-//   CHECK-DAG: %[[U3:.*]] = tensor.dim %[[A]], %[[C2]] : tensor<?x?x?xf64>
-//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<3xi8>
-//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<3xindex>
-//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<3xindex>
-//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<3xi8> to memref<?xi8>
-//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<3xindex> to memref<?xindex>
-//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<3xindex> to memref<?xindex>
-//       CHECK: %[[NP:.*]] = llvm.mlir.null : !llvm.ptr<i8>
-//       CHECK: %[[C:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[EmptyCOO]], %[[NP]])
-//       CHECK: %[[M:.*]] = memref.alloca() : memref<3xindex>
-//       CHECK: %[[N:.*]] = memref.cast %[[M]] : memref<3xindex> to memref<?xindex>
-//       CHECK: %[[BUF:.*]] = memref.alloca() : memref<f64>
-//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %[[U1]] step %[[C1]] {
-//       CHECK:   scf.for %[[J:.*]] = %[[C0]] to %[[U2]] step %[[C1]] {
-//       CHECK:     scf.for %[[K:.*]] = %[[C0]] to %[[U3]] step %[[C1]] {
-//       CHECK:       %[[E:.*]] = tensor.extract %[[A]][%[[I]], %[[J]], %[[K]]] : tensor<?x?x?xf64>
-//       CHECK:       memref.store %[[I]], %[[M]][%[[C0]]] : memref<3xindex>
-//       CHECK:       memref.store %[[J]], %[[M]][%[[C1]]] : memref<3xindex>
-//       CHECK:       memref.store %[[K]], %[[M]][%[[C2]]] : memref<3xindex>
-//       CHECK:       memref.store %[[E]], %[[BUF]][] : memref<f64>
-//       CHECK:       call @addEltF64(%[[C]], %[[BUF]], %[[N]], %[[Z]])
-//       CHECK:     }
-//       CHECK:   }
-//       CHECK: }
-//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[FromCOO]], %[[C]])
-//       CHECK: call @delSparseTensorCOOF64(%[[C]])
-//       CHECK: return %[[T]] : !llvm.ptr<i8>
-func.func @sparse_convert_3d(%arg0: tensor<?x?x?xf64>) -> tensor<?x?x?xf64, #SparseTensor> {
-  %0 = sparse_tensor.convert %arg0 : tensor<?x?x?xf64> to tensor<?x?x?xf64, #SparseTensor>
-  return %0 : tensor<?x?x?xf64, #SparseTensor>
-}
-
 // CHECK-LABEL: func @sparse_pointers(
 //  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>)
 //       CHECK: %[[C:.*]] = arith.constant 0 : index
diff --git a/mlir/test/Dialect/SparseTensor/convert_dense2sparse.mlir b/mlir/test/Dialect/SparseTensor/convert_dense2sparse.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Dialect/SparseTensor/convert_dense2sparse.mlir
@@ -0,0 +1,182 @@
+// RUN: mlir-opt %s --sparse-tensor-conversion --canonicalize --cse | FileCheck %s
+
+#SparseVector = #sparse_tensor.encoding<{
+  dimLevelType = ["compressed"]
+}>
+
+#CSR = #sparse_tensor.encoding<{
+  dimLevelType = ["dense", "compressed"]
+}>
+
+#SparseTensor = #sparse_tensor.encoding<{
+  dimLevelType = ["dense", "compressed", "compressed"],
+  dimOrdering = affine_map<(i,j,k) -> (k,i,j)>
+}>
+
+// CHECK-LABEL: func @sparse_convert_1d(
+//  CHECK-SAME: %[[A:.*]]: tensor<?xi32>) -> !llvm.ptr<i8> {
+//   CHECK-DAG: %[[EmptyCOO:.*]] = arith.constant 4 : i32
+//   CHECK-DAG: %[[FromCOO:.*]] = arith.constant 2 : i32
+//   CHECK-DAG: %[[I0:.*]] = arith.constant 0 : i32
+//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
+//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
+//   CHECK-DAG: %[[U:.*]] = tensor.dim %[[A]], %[[C0]] : tensor<?xi32>
+//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<1xi8>
+//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<1xindex>
+//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<1xindex>
+//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<1xi8> to memref<?xi8>
+//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<1xindex> to memref<?xindex>
+//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<1xindex> to memref<?xindex>
+//       CHECK: %[[NP:.*]] = llvm.mlir.null : !llvm.ptr<i8>
+//       CHECK: %[[C:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[EmptyCOO]], %[[NP]])
+//       CHECK: %[[M:.*]] = memref.alloca() : memref<1xindex>
+//       CHECK: %[[T:.*]] = memref.cast %[[M]] : memref<1xindex> to memref<?xindex>
+//       CHECK: %[[BUF:.*]] = memref.alloca() : memref<i32>
+//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %[[U]] step %[[C1]] {
+//       CHECK:   %[[E:.*]] = tensor.extract %[[A]][%[[I]]] : tensor<?xi32>
+//       CHECK:   %[[N:.*]] = arith.cmpi ne, %[[E]], %[[I0]] : i32
+//       CHECK:   scf.if %[[N]] {
+//       CHECK:     memref.store %[[I]], %[[M]][%[[C0]]] : memref<1xindex>
+//       CHECK:     memref.store %[[E]], %[[BUF]][] : memref<i32>
+//       CHECK:     call @addEltI32(%[[C]], %[[BUF]], %[[T]], %[[Z]])
+//       CHECK:   }
+//       CHECK: }
+//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[FromCOO]], %[[C]])
+//       CHECK: call @delSparseTensorCOOI32(%[[C]])
+//       CHECK: return %[[T]] : !llvm.ptr<i8>
+func.func @sparse_convert_1d(%arg0: tensor<?xi32>) -> tensor<?xi32, #SparseVector> {
+  %0 = sparse_tensor.convert %arg0 : tensor<?xi32> to tensor<?xi32, #SparseVector>
+  return %0 : tensor<?xi32, #SparseVector>
+}
+
+// CHECK-LABEL: func @sparse_convert_complex(
+//  CHECK-SAME: %[[A:.*]]: tensor<100xcomplex<f64>>) -> !llvm.ptr<i8> {
+//   CHECK-DAG: %[[CC:.*]] = complex.constant [0.000000e+00, 0.000000e+00] : complex<f64>
+//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
+//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
+//   CHECK-DAG: %[[C100:.*]] = arith.constant 100 : index
+//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %[[C100]] step %[[C1]] {
+//       CHECK:   %[[E:.*]] = tensor.extract %[[A]][%[[I]]] : tensor<100xcomplex<f64>>
+//       CHECK:   %[[N:.*]] = complex.neq %[[E]], %[[CC]] : complex<f64>
+//       CHECK:   scf.if %[[N]] {
+//       CHECK:     memref.store %[[I]], %{{.*}}[%[[C0]]] : memref<1xindex>
+//       CHECK:     call @addEltC64
+//       CHECK:   }
+//       CHECK: }
+//       CHECK: %[[T:.*]] = call @newSparseTensor
+//       CHECK: call @delSparseTensorCOOC64
+//       CHECK: return %[[T]] : !llvm.ptr<i8>
+func.func @sparse_convert_complex(%arg0: tensor<100xcomplex<f64>>) -> tensor<100xcomplex<f64>, #SparseVector> {
+  %0 = sparse_tensor.convert %arg0 : tensor<100xcomplex<f64>> to tensor<100xcomplex<f64>, #SparseVector>
+  return %0 : tensor<100xcomplex<f64>, #SparseVector>
+}
+
+// CHECK-LABEL: func @sparse_convert_2d(
+//  CHECK-SAME: %[[A:.*]]: tensor<2x4xf64>) -> !llvm.ptr<i8>
+//   CHECK-DAG: %[[EmptyCOO:.*]] = arith.constant 4 : i32
+//   CHECK-DAG: %[[FromCOO:.*]] = arith.constant 2 : i32
+//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
+//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
+//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<2xi8>
+//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<2xindex>
+//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<2xindex>
+//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<2xi8> to memref<?xi8>
+//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<2xindex> to memref<?xindex>
+//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<2xindex> to memref<?xindex>
+//       CHECK: %[[NP:.*]] = llvm.mlir.null : !llvm.ptr<i8>
+//       CHECK: %[[C:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[EmptyCOO]], %[[NP]])
+//       CHECK: %[[M:.*]] = memref.alloca() : memref<2xindex>
+//       CHECK: %[[T:.*]] = memref.cast %[[M]] : memref<2xindex> to memref<?xindex>
+//       CHECK: %[[BUF:.*]] = memref.alloca() : memref<f64>
+//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %{{.*}} step %[[C1]] {
+//       CHECK:   scf.for %[[J:.*]] = %[[C0]] to %{{.*}} step %[[C1]] {
+//       CHECK:     %[[E:.*]] = tensor.extract %[[A]][%[[I]], %[[J]]] : tensor<2x4xf64>
+//       CHECK:     memref.store %[[I]], %[[M]][%[[C0]]] : memref<2xindex>
+//       CHECK:     memref.store %[[J]], %[[M]][%[[C1]]] : memref<2xindex>
+//       CHECK:     memref.store %[[E]], %[[BUF]][] : memref<f64>
+//       CHECK:     call @addEltF64(%[[C]], %[[BUF]], %[[T]], %[[Z]])
+//       CHECK:   }
+//       CHECK: }
+//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[FromCOO]], %[[C]])
+//       CHECK: call @delSparseTensorCOOF64(%[[C]])
+//       CHECK: return %[[T]] : !llvm.ptr<i8>
+func.func @sparse_convert_2d(%arg0: tensor<2x4xf64>) -> tensor<2x4xf64, #CSR> {
+  %0 = sparse_tensor.convert %arg0 : tensor<2x4xf64> to tensor<2x4xf64, #CSR>
+  return %0 : tensor<2x4xf64, #CSR>
+}
+
+// CHECK-LABEL: func @sparse_constant() -> !llvm.ptr<i8> {
+//   CHECK-DAG: %[[EmptyCOO:.*]] = arith.constant 4 : i32
+//   CHECK-DAG: %[[FromCOO:.*]] = arith.constant 2 : i32
+//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
+//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
+//   CHECK-DAG: %[[C2:.*]] = arith.constant 2 : index
+//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<2xi8>
+//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<2xindex>
+//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<2xindex>
+//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<2xi8> to memref<?xi8>
+//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<2xindex> to memref<?xindex>
+//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<2xindex> to memref<?xindex>
+//       CHECK: %[[NP:.*]] = llvm.mlir.null : !llvm.ptr<i8>
+//       CHECK: %[[C:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[EmptyCOO]], %[[NP]])
+//       CHECK: %[[M:.*]] = memref.alloca() : memref<2xindex>
+//       CHECK: %[[N:.*]] = memref.cast %[[M]] : memref<2xindex> to memref<?xindex>
+//       CHECK: %[[BUF:.*]] = memref.alloca() : memref<f32>
+//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %[[C2]] step %[[C1]] {
+//       CHECK:   memref.store %{{.*}}, %[[M]][%[[C0]]] : memref<2xindex>
+//       CHECK:   memref.store %{{.*}}, %[[M]][%[[C1]]] : memref<2xindex>
+//       CHECK:   %[[V:.*]] = tensor.extract %{{.*}}[%[[I]]] : tensor<2xf32>
+//       CHECK:   memref.store %[[V]], %[[BUF]][] : memref<f32>
+//       CHECK:   call @addEltF32(%{{.*}}, %[[BUF]], %[[N]], %{{.*}})
+//       CHECK: }
+//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[FromCOO]], %[[C]])
+//       CHECK: call @delSparseTensorCOOF32(%[[C]])
+//       CHECK: return %[[T]] : !llvm.ptr<i8>
+func.func @sparse_constant() -> tensor<8x7xf32, #CSR>{
+  // Initialize a tensor.
+  %0 = arith.constant sparse<[[0, 0], [1, 6]], [1.0, 5.0]> : tensor<8x7xf32>
+  // Convert the tensor to a sparse tensor.
+  %1 = sparse_tensor.convert %0 : tensor<8x7xf32> to tensor<8x7xf32, #CSR>
+  return %1 : tensor<8x7xf32, #CSR>
+}
+
+// CHECK-LABEL: func @sparse_convert_3d(
+//  CHECK-SAME: %[[A:.*]]: tensor<?x?x?xf64>) -> !llvm.ptr<i8>
+//   CHECK-DAG: %[[EmptyCOO:.*]] = arith.constant 4 : i32
+//   CHECK-DAG: %[[FromCOO:.*]] = arith.constant 2 : i32
+//   CHECK-DAG: %[[C0:.*]] = arith.constant 0 : index
+//   CHECK-DAG: %[[C1:.*]] = arith.constant 1 : index
+//   CHECK-DAG: %[[C2:.*]] = arith.constant 2 : index
+//   CHECK-DAG: %[[U1:.*]] = tensor.dim %[[A]], %[[C0]] : tensor<?x?x?xf64>
+//   CHECK-DAG: %[[U2:.*]] = tensor.dim %[[A]], %[[C1]] : tensor<?x?x?xf64>
+//   CHECK-DAG: %[[U3:.*]] = tensor.dim %[[A]], %[[C2]] : tensor<?x?x?xf64>
+//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<3xi8>
+//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<3xindex>
+//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<3xindex>
+//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<3xi8> to memref<?xi8>
+//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<3xindex> to memref<?xindex>
+//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<3xindex> to memref<?xindex>
+//       CHECK: %[[NP:.*]] = llvm.mlir.null : !llvm.ptr<i8>
+//       CHECK: %[[C:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[EmptyCOO]], %[[NP]])
+//       CHECK: %[[M:.*]] = memref.alloca() : memref<3xindex>
+//       CHECK: %[[N:.*]] = memref.cast %[[M]] : memref<3xindex> to memref<?xindex>
+//       CHECK: %[[BUF:.*]] = memref.alloca() : memref<f64>
+//       CHECK: scf.for %[[I:.*]] = %[[C0]] to %[[U1]] step %[[C1]] {
+//       CHECK:   scf.for %[[J:.*]] = %[[C0]] to %[[U2]] step %[[C1]] {
+//       CHECK:     scf.for %[[K:.*]] = %[[C0]] to %[[U3]] step %[[C1]] {
+//       CHECK:       %[[E:.*]] = tensor.extract %[[A]][%[[I]], %[[J]], %[[K]]] : tensor<?x?x?xf64>
+//       CHECK:       memref.store %[[I]], %[[M]][%[[C0]]] : memref<3xindex>
+//       CHECK:       memref.store %[[J]], %[[M]][%[[C1]]] : memref<3xindex>
+//       CHECK:       memref.store %[[K]], %[[M]][%[[C2]]] : memref<3xindex>
+//       CHECK:       memref.store %[[E]], %[[BUF]][] : memref<f64>
+//       CHECK:       call @addEltF64(%[[C]], %[[BUF]], %[[N]], %[[Z]])
+//       CHECK:     }
+//       CHECK:   }
+//       CHECK: }
+//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[FromCOO]], %[[C]])
+//       CHECK: call @delSparseTensorCOOF64(%[[C]])
+//       CHECK: return %[[T]] : !llvm.ptr<i8>
+func.func @sparse_convert_3d(%arg0: tensor<?x?x?xf64>) -> tensor<?x?x?xf64, #SparseTensor> {
+  %0 = sparse_tensor.convert %arg0 : tensor<?x?x?xf64> to tensor<?x?x?xf64, #SparseTensor>
+  return %0 : tensor<?x?x?xf64, #SparseTensor>
+}
diff --git a/mlir/test/Dialect/SparseTensor/conversion_sparse2dense.mlir b/mlir/test/Dialect/SparseTensor/convert_sparse2dense.mlir
rename from mlir/test/Dialect/SparseTensor/conversion_sparse2dense.mlir
rename to mlir/test/Dialect/SparseTensor/convert_sparse2dense.mlir
diff --git a/mlir/test/Dialect/SparseTensor/conversion_sparse2sparse.mlir b/mlir/test/Dialect/SparseTensor/convert_sparse2sparse.mlir
rename from mlir/test/Dialect/SparseTensor/conversion_sparse2sparse.mlir
rename to mlir/test/Dialect/SparseTensor/convert_sparse2sparse.mlir
--- a/mlir/test/Dialect/SparseTensor/conversion_sparse2sparse.mlir
+++ b/mlir/test/Dialect/SparseTensor/convert_sparse2sparse.mlir
@@ -4,7 +4,7 @@
 //
 // Now again with `kAuto` (the new default).
 // RUN: mlir-opt %s --sparse-tensor-conversion="s2s-strategy=0" \
-// RUN:    --canonicalize --cse | FileCheck %s -check-prefix=CHECK-AUTO
+// RUN:    --canonicalize --cse | FileCheck %s -check-prefixes=CHECK-AUTO,CHECK
 
 #SparseVector64 = #sparse_tensor.encoding<{
   dimLevelType = ["compressed"],
@@ -18,6 +18,42 @@
   indexBitWidth = 32
 }>
 
+#SparseVector = #sparse_tensor.encoding<{
+  dimLevelType = ["compressed"]
+}>
+
+// CHECK-LABEL: func @sparse_nop_convert(
+//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>) -> !llvm.ptr<i8>
+//       CHECK: return %[[A]] : !llvm.ptr<i8>
+func.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_hidden_nop_cast(
+//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>) -> !llvm.ptr<i8>
+//       CHECK: return %[[A]] : !llvm.ptr<i8>
+func.func @sparse_hidden_nop_cast(%arg0: tensor<32xf32, #SparseVector>) -> tensor<?xf32, #SparseVector> {
+  %0 = sparse_tensor.convert %arg0 : tensor<32xf32, #SparseVector> to tensor<?xf32, #SparseVector>
+  return %0 : tensor<?xf32, #SparseVector>
+}
+
+// CHECK-LABEL: func @sparse_convert_1d_ss(
+//  CHECK-SAME: %[[A:.*]]: !llvm.ptr<i8>)
+//   CHECK-DAG: %[[SparseToSparse:.*]] = arith.constant 3 : i32
+//   CHECK-DAG: %[[P:.*]] = memref.alloca() : memref<1xi8>
+//   CHECK-DAG: %[[Q:.*]] = memref.alloca() : memref<1xindex>
+//   CHECK-DAG: %[[R:.*]] = memref.alloca() : memref<1xindex>
+//   CHECK-DAG: %[[X:.*]] = memref.cast %[[P]] : memref<1xi8> to memref<?xi8>
+//   CHECK-DAG: %[[Y:.*]] = memref.cast %[[Q]] : memref<1xindex> to memref<?xindex>
+//   CHECK-DAG: %[[Z:.*]] = memref.cast %[[R]] : memref<1xindex> to memref<?xindex>
+//       CHECK: %[[T:.*]] = call @newSparseTensor(%[[X]], %[[Y]], %[[Z]], %{{.*}}, %{{.*}}, %{{.*}}, %[[SparseToSparse]], %[[A]])
+//       CHECK: return %[[T]] : !llvm.ptr<i8>
+func.func @sparse_convert_1d_ss(%arg0: tensor<?xf32, #SparseVector64>) -> tensor<?xf32, #SparseVector32> {
+  %0 = sparse_tensor.convert %arg0 : tensor<?xf32, #SparseVector64> to tensor<?xf32, #SparseVector32>
+  return %0 : tensor<?xf32, #SparseVector32>
+}
+
 // CHECK-COO-LABEL: func @sparse_convert(
 //  CHECK-COO-SAME: %[[A:.*]]: !llvm.ptr<i8>)
 //  CHECK-COO-DAG:  %[[ToCOO:.*]] = arith.constant 5 : i32