diff --git a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorConversion.cpp b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorConversion.cpp
--- a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorConversion.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorConversion.cpp
@@ -573,8 +573,22 @@
   rewriter.create<scf::ConditionOp>(loc, cond, before->getArguments());
   Block *after = rewriter.createBlock(&whileOp.getAfter(), {}, noTypes);
   rewriter.setInsertionPointToStart(after);
+
+  bool hasDenseDim = llvm::any_of(
+      enc.getDimLevelType(), [](DimLevelType dlt) { return isDenseDLT(dlt); });
+  if (hasDenseDim) {
+    Value elemV = rewriter.create<memref::LoadOp>(loc, elemPtr);
+    Value isZero = genIsNonzero(rewriter, loc, elemV);
+    scf::IfOp ifOp = rewriter.create<scf::IfOp>(loc, isZero, /*else*/ false);
+    rewriter.setInsertionPointToStart(&ifOp.getThenRegion().front());
+  }
   // Callback here to build loop body.
   bodyBuilder(rewriter, loc, srcIdx, elemPtr);
+
+  // Exit the scope from the IfOp.
+  if (hasDenseDim)
+    rewriter.setInsertionPointToEnd(after);
+
   rewriter.create<scf::YieldOp>(loc);
   // Finish generating loop.
   rewriter.setInsertionPointAfter(whileOp);
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/concatenate.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/concatenate.mlir
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/concatenate.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/concatenate.mlir
@@ -169,9 +169,12 @@
     %v = vector.transfer_read %c[%c0, %c0], %du: tensor<9x4xf64>, vector<9x4xf64>
     vector.print %v : vector<9x4xf64>
 
+    %n = sparse_tensor.number_of_entries %A : tensor<9x4xf64, #MAT_C_C>
+    vector.print %n : index
+
     %1 = sparse_tensor.values %A : tensor<9x4xf64, #MAT_C_C> to memref<?xf64>
-    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<36xf64>
-    vector.print %2 : vector<36xf64>
+    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<18xf64>
+    vector.print %2 : vector<18xf64>
 
     return
   }
@@ -184,9 +187,12 @@
     %v = vector.transfer_read %c[%c0, %c0], %du: tensor<9x4xf64>, vector<9x4xf64>
     vector.print %v : vector<9x4xf64>
 
+    %n = sparse_tensor.number_of_entries %A : tensor<9x4xf64, #MAT_C_C_P>
+    vector.print %n : index
+
     %1 = sparse_tensor.values %A : tensor<9x4xf64, #MAT_C_C_P> to memref<?xf64>
-    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<36xf64>
-    vector.print %2 : vector<36xf64>
+    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<18xf64>
+    vector.print %2 : vector<18xf64>
 
     return
   }
@@ -209,9 +215,12 @@
     %v = vector.transfer_read %c[%c0, %c0], %du: tensor<4x9xf64>, vector<4x9xf64>
     vector.print %v : vector<4x9xf64>
 
+    %n = sparse_tensor.number_of_entries %A : tensor<4x9xf64, #MAT_C_C>
+    vector.print %n : index
+
     %1 = sparse_tensor.values %A : tensor<4x9xf64, #MAT_C_C> to memref<?xf64>
-    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<36xf64>
-    vector.print %2 : vector<36xf64>
+    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<18xf64>
+    vector.print %2 : vector<18xf64>
 
     return
   }
@@ -224,9 +233,12 @@
     %v = vector.transfer_read %c[%c0, %c0], %du: tensor<?x?xf64>, vector<4x9xf64>
     vector.print %v : vector<4x9xf64>
 
+    %n = sparse_tensor.number_of_entries %A : tensor<?x?xf64, #MAT_C_C>
+    vector.print %n : index
+
     %1 = sparse_tensor.values %A : tensor<?x?xf64, #MAT_C_C> to memref<?xf64>
-    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<36xf64>
-    vector.print %2 : vector<36xf64>
+    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<18xf64>
+    vector.print %2 : vector<18xf64>
 
     return
   }
@@ -239,9 +251,12 @@
     %v = vector.transfer_read %c[%c0, %c0], %du: tensor<4x9xf64>, vector<4x9xf64>
     vector.print %v : vector<4x9xf64>
 
+    %n = sparse_tensor.number_of_entries %A : tensor<4x9xf64, #MAT_C_C_P>
+    vector.print %n : index
+
     %1 = sparse_tensor.values %A : tensor<4x9xf64, #MAT_C_C_P> to memref<?xf64>
-    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<36xf64>
-    vector.print %2 : vector<36xf64>
+    %2 = vector.transfer_read %1[%c0], %du: memref<?xf64>, vector<18xf64>
+    vector.print %2 : vector<18xf64>
 
     return
   }
@@ -297,7 +312,8 @@
     %sm44dc_dyn = sparse_tensor.convert %m44 : tensor<4x4xf64> to tensor<?x?xf64, #MAT_D_C>
 
     // CHECK:    ( ( 1, 0, 3, 0 ), ( 0, 2, 0, 0 ), ( 1, 0, 1, 1 ), ( 0, 0.5, 0, 0 ), ( 1, 5, 2, 0 ), ( 0, 0, 1.5, 1 ), ( 0, 3.5, 0, 0 ), ( 1, 5, 2, 0 ), ( 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 3, 2, 1, 0, 1, 1, 0, 0.5, 0, 0, 1, 5, 2, 0, 1.5, 1, 3.5, 1, 5, 2, 1, 0.5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 3, 2, 1, 1, 1, 0.5, 1, 5, 2, 1.5, 1, 3.5, 1, 5, 2, 1, 0.5 )
     %0 = call @concat_sparse_sparse(%sm24cc, %sm34cd, %sm44dc)
                : (tensor<2x4xf64, #MAT_C_C>, tensor<3x4xf64, #MAT_C_D>, tensor<4x4xf64, #MAT_D_C>) -> tensor<9x4xf64, #MAT_C_C>
     call @dump_mat_9x4(%0) : (tensor<9x4xf64, #MAT_C_C>) -> ()
@@ -308,7 +324,8 @@
     call @dump_mat_dense_9x4(%1) : (tensor<9x4xf64>) -> ()
 
     // CHECK-NEXT: ( ( 1, 0, 3, 0 ), ( 0, 2, 0, 0 ), ( 1, 0, 1, 1 ), ( 0, 0.5, 0, 0 ), ( 1, 5, 2, 0 ), ( 0, 0, 1.5, 1 ), ( 0, 3.5, 0, 0 ), ( 1, 5, 2, 0 ), ( 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 3, 2, 1, 0, 1, 1, 0, 0.5, 0, 0, 1, 5, 2, 0, 1.5, 1, 3.5, 1, 5, 2, 1, 0.5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 3, 2, 1, 1, 1, 0.5, 1, 5, 2, 1.5, 1, 3.5, 1, 5, 2, 1, 0.5 )
     %2 = call @concat_mix_sparse(%m24, %sm34cd, %sm44dc)
                : (tensor<2x4xf64>, tensor<3x4xf64, #MAT_C_D>, tensor<4x4xf64, #MAT_D_C>) -> tensor<9x4xf64, #MAT_C_C>
     call @dump_mat_9x4(%2) : (tensor<9x4xf64, #MAT_C_C>) -> ()
@@ -319,7 +336,8 @@
     call @dump_mat_dense_9x4(%3) : (tensor<9x4xf64>) -> ()
 
     // CHECK-NEXT: ( ( 1, 0, 3, 0 ), ( 0, 2, 0, 0 ), ( 1, 0, 1, 1 ), ( 0, 0.5, 0, 0 ), ( 1, 5, 2, 0 ), ( 0, 0, 1.5, 1 ), ( 0, 3.5, 0, 0 ), ( 1, 5, 2, 0 ), ( 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 1, 0, 1, 1, 1, 2, 0, 0.5, 5, 3.5, 5, 0.5, 3, 1, 0, 2, 1.5, 2, 1, 0, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 1, 1, 1, 1, 2, 0.5, 5, 3.5, 5, 0.5, 3, 1, 2, 1.5, 2, 1, 1 )
     %4 = call @concat_sparse_sparse_perm(%sm24ccp, %sm34cd, %sm44dc)
                : (tensor<2x4xf64, #MAT_C_C_P>, tensor<3x4xf64, #MAT_C_D>, tensor<4x4xf64, #MAT_D_C>) -> tensor<9x4xf64, #MAT_C_C_P>
     call @dump_mat_perm_9x4(%4) : (tensor<9x4xf64, #MAT_C_C_P>) -> ()
@@ -330,7 +348,8 @@
     call @dump_mat_dense_9x4(%5) : (tensor<9x4xf64>) -> ()
 
     // CHECK-NEXT: ( ( 1, 0, 3, 0 ), ( 0, 2, 0, 0 ), ( 1, 0, 1, 1 ), ( 0, 0.5, 0, 0 ), ( 1, 5, 2, 0 ), ( 0, 0, 1.5, 1 ), ( 0, 3.5, 0, 0 ), ( 1, 5, 2, 0 ), ( 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 3, 2, 1, 0, 1, 1, 0, 0.5, 0, 0, 1, 5, 2, 0, 1.5, 1, 3.5, 1, 5, 2, 1, 0.5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 3, 2, 1, 1, 1, 0.5, 1, 5, 2, 1.5, 1, 3.5, 1, 5, 2, 1, 0.5 )
     %6 = call @concat_mix_sparse_perm(%m24, %sm34cdp, %sm44dc)
                : (tensor<2x4xf64>, tensor<3x4xf64, #MAT_C_D_P>, tensor<4x4xf64, #MAT_D_C>) -> tensor<9x4xf64, #MAT_C_C>
     call @dump_mat_9x4(%6) : (tensor<9x4xf64, #MAT_C_C>) -> ()
@@ -341,7 +360,8 @@
     call @dump_mat_dense_9x4(%7) : (tensor<9x4xf64>) -> ()
 
     // CHECK-NEXT: ( ( 1, 0, 1, 0, 1, 0, 0, 1.5, 1 ), ( 3.1, 0, 1, 0, 0.5, 0, 3.5, 0, 0 ), ( 0, 2, 0, 0, 1, 1, 5, 2, 0 ), ( 0, 0, 5, 2, 0, 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 1, 0, 1, 1.5, 1, 3.1, 1, 0, 0.5, 3.5, 2, 0, 0, 1, 1, 5, 2, 5, 2, 0, 1, 0.5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 1, 1, 1.5, 1, 3.1, 1, 0.5, 3.5, 2, 1, 1, 5, 2, 5, 2, 1, 0.5 )
     %8 = call @concat_sparse_sparse_dim1(%sm42cc, %sm43cd, %sm44dc)
                : (tensor<4x2xf64, #MAT_C_C>, tensor<4x3xf64, #MAT_C_D>, tensor<4x4xf64, #MAT_D_C>) -> tensor<4x9xf64, #MAT_C_C>
     call @dump_mat_4x9(%8) : (tensor<4x9xf64, #MAT_C_C>) -> ()
@@ -352,7 +372,8 @@
     call @dump_mat_dense_4x9(%9) : (tensor<4x9xf64>) -> ()
 
     // CHECK-NEXT: ( ( 1, 0, 1, 0, 1, 0, 0, 1.5, 1 ), ( 3.1, 0, 1, 0, 0.5, 0, 3.5, 0, 0 ), ( 0, 2, 0, 0, 1, 1, 5, 2, 0 ), ( 0, 0, 5, 2, 0, 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 1, 0, 1, 1.5, 1, 3.1, 1, 0, 0.5, 3.5, 2, 0, 0, 1, 1, 5, 2, 5, 2, 0, 1, 0.5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 1, 1, 1.5, 1, 3.1, 1, 0.5, 3.5, 2, 1, 1, 5, 2, 5, 2, 1, 0.5 )
     %10 = call @concat_mix_sparse_dim1(%m42, %sm43cd, %sm44dc)
                : (tensor<4x2xf64>, tensor<4x3xf64, #MAT_C_D>, tensor<4x4xf64, #MAT_D_C>) -> tensor<4x9xf64, #MAT_C_C>
     call @dump_mat_4x9(%10) : (tensor<4x9xf64, #MAT_C_C>) -> ()
@@ -363,7 +384,8 @@
     call @dump_mat_dense_4x9(%11) : (tensor<4x9xf64>) -> ()
 
     // CHECK-NEXT: ( ( 1, 0, 1, 0, 1, 0, 0, 1.5, 1 ), ( 3.1, 0, 1, 0, 0.5, 0, 3.5, 0, 0 ), ( 0, 2, 0, 0, 1, 1, 5, 2, 0 ), ( 0, 0, 5, 2, 0, 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 3.1, 2, 1, 1, 0, 5, 0, 0, 0, 2, 1, 0.5, 1, 0, 1, 1, 3.5, 5, 0.5, 1.5, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 3.1, 2, 1, 1, 5, 2, 1, 0.5, 1, 1, 1, 3.5, 5, 0.5, 1.5, 2, 1 )
     %12 = call @concat_sparse_sparse_perm_dim1(%sm42ccp, %sm43cd, %sm44dc)
                : (tensor<4x2xf64, #MAT_C_C_P>, tensor<4x3xf64, #MAT_C_D>, tensor<4x4xf64, #MAT_D_C>) -> tensor<4x9xf64, #MAT_C_C_P>
     call @dump_mat_perm_4x9(%12) : (tensor<4x9xf64, #MAT_C_C_P>) -> ()
@@ -374,7 +396,8 @@
     call @dump_mat_dense_4x9(%13) : (tensor<4x9xf64>) -> ()
 
     // CHECK-NEXT: ( ( 1, 0, 1, 0, 1, 0, 0, 1.5, 1 ), ( 3.1, 0, 1, 0, 0.5, 0, 3.5, 0, 0 ), ( 0, 2, 0, 0, 1, 1, 5, 2, 0 ), ( 0, 0, 5, 2, 0, 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 1, 0, 1, 1.5, 1, 3.1, 1, 0, 0.5, 3.5, 2, 0, 0, 1, 1, 5, 2, 5, 2, 0, 1, 0.5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 1, 1, 1.5, 1, 3.1, 1, 0.5, 3.5, 2, 1, 1, 5, 2, 5, 2, 1, 0.5 )
     %14 = call @concat_mix_sparse_perm_dim1(%m42, %sm43cdp, %sm44dc)
                : (tensor<4x2xf64>, tensor<4x3xf64, #MAT_C_D_P>, tensor<4x4xf64, #MAT_D_C>) -> tensor<4x9xf64, #MAT_C_C>
     call @dump_mat_4x9(%14) : (tensor<4x9xf64, #MAT_C_C>) -> ()
@@ -385,7 +408,8 @@
     call @dump_mat_dense_4x9(%15) : (tensor<4x9xf64>) -> ()
 
     // CHECK-NEXT: ( ( 1, 0, 1, 0, 1, 0, 0, 1.5, 1 ), ( 3.1, 0, 1, 0, 0.5, 0, 3.5, 0, 0 ), ( 0, 2, 0, 0, 1, 1, 5, 2, 0 ), ( 0, 0, 5, 2, 0, 1, 0.5, 0, 0 ) )
-    // CHECK-NEXT: ( 1, 1, 0, 1, 1.5, 1, 3.1, 1, 0, 0.5, 3.5, 2, 0, 0, 1, 1, 5, 2, 5, 2, 0, 1, 0.5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )
+    // CHECK-NEXT: 18
+    // CHECK-NEXT: ( 1, 1, 1, 1.5, 1, 3.1, 1, 0.5, 3.5, 2, 1, 1, 5, 2, 5, 2, 1, 0.5 )
     %16 = call @concat_mix_sparse_dyn(%m42, %sm43cd, %sm44dc)
                : (tensor<4x2xf64>, tensor<4x3xf64, #MAT_C_D>, tensor<4x4xf64, #MAT_D_C>) -> tensor<?x?xf64, #MAT_C_C>
     call @dump_mat_dyn(%16) : (tensor<?x?xf64, #MAT_C_C>) -> ()