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
@@ -74,15 +74,17 @@
 }
 
 def SparseTensor_ConvertOp : SparseTensor_Op<"convert",
-  [NoSideEffect, SameOperandsAndResultType]>,
+  [NoSideEffect, SameOperandsAndResultElementType]>,
     Arguments<(ins AnyTensor:$source)>,
     Results<(outs AnyTensor:$dest)> {
   string summary = "Converts between different tensor types";
   string description = [{
     Converts one sparse or dense tensor type to another tensor type. The rank
-    and dimensions of the source and destination types must match, but the sparse
-    encoding of these types can obviously be different. The name `convert` was
-    preferred over `cast`, since the operation may incur a non-trivial cost.
+    of the source and destination types must match exactly, and the dimension
+    sizes must either match exactly or relax from a static to a dynamic size.
+    The sparse encoding of the two types can obviously be completely different.
+    The name `convert` was preferred over `cast`, since the operation may incur
+    a non-trivial cost.
 
     When converting between two different sparse tensor types, only explicitly
     stored values are moved from one underlying sparse storage format to
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
@@ -237,7 +237,8 @@
 static LogicalResult verify(ConvertOp op) {
   if (auto tp1 = op.source().getType().dyn_cast<RankedTensorType>()) {
     if (auto tp2 = op.dest().getType().dyn_cast<RankedTensorType>()) {
-      assert(tp1.getRank() == tp2.getRank());
+      if (tp1.getRank() != tp2.getRank())
+        return op.emitError("unexpected conversion mismatch in rank");
       auto shape1 = tp1.getShape();
       auto shape2 = tp2.getShape();
       // Accept size matches between the source and the destination type
diff --git a/mlir/test/Dialect/SparseTensor/invalid.mlir b/mlir/test/Dialect/SparseTensor/invalid.mlir
--- a/mlir/test/Dialect/SparseTensor/invalid.mlir
+++ b/mlir/test/Dialect/SparseTensor/invalid.mlir
@@ -160,9 +160,19 @@
 
 // -----
 
+#DCSR = #sparse_tensor.encoding<{dimLevelType = ["compressed", "compressed"]}>
+
+func @sparse_convert_rank_mismatch(%arg0: tensor<10x10xf64, #DCSR>) -> tensor<?xf64> {
+  // expected-error@+1 {{unexpected conversion mismatch in rank}}
+  %0 = sparse_tensor.convert %arg0 : tensor<10x10xf64, #DCSR> to tensor<?xf64>
+  return %0 : tensor<?xf64>
+}
+
+// -----
+
 #CSR = #sparse_tensor.encoding<{dimLevelType = ["dense", "compressed"]}>
 
-func @sparse_convert_mismatch(%arg0: tensor<10x?xf32>) -> tensor<10x10xf32, #CSR> {
+func @sparse_convert_dim_mismatch(%arg0: tensor<10x?xf32>) -> tensor<10x10xf32, #CSR> {
   // expected-error@+1 {{unexpected conversion mismatch in dimension 1}}
   %0 = sparse_tensor.convert %arg0 : tensor<10x?xf32> to tensor<10x10xf32, #CSR>
   return %0 : tensor<10x10xf32, #CSR>