diff --git a/mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h b/mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h
--- a/mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h
+++ b/mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h
@@ -432,8 +432,15 @@
   /// Sets the level number and level-type of the `t`th tensor on
   /// `i`th loop.
   void setLevelAndType(TensorId t, LoopId i, Level lvl, DimLevelType dlt) {
-    assert(t < numTensors && i < numLoops && lvl < lvlToLoop[t].size() &&
-           isValidDLT(dlt));
+    assert(t < numTensors && i < numLoops && isValidDLT(dlt));
+    // In case with indexing map like (d0) -> (0, d0), there might be more
+    // levels then loops because of the constant index.
+    // TODO: Constant indices are currently not support on sparse tensor, but
+    // are allowed in non-annotated dense tensor. Support it, it would be
+    // required for sparse tensor slice rank reducing too.
+    if (lvl >= lvlToLoop[t].size())
+      lvlToLoop[t].resize(lvl + 1);
+
     lvlTypes[t][i] = dlt;
     loopToLvl[t][i] = lvl;
     lvlToLoop[t][lvl] = i;
diff --git a/mlir/lib/Dialect/SparseTensor/Transforms/CodegenEnv.cpp b/mlir/lib/Dialect/SparseTensor/Transforms/CodegenEnv.cpp
--- a/mlir/lib/Dialect/SparseTensor/Transforms/CodegenEnv.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Transforms/CodegenEnv.cpp
@@ -86,10 +86,13 @@
   SmallVector<Value> tensors; // input tensors passed to loop emitter
   for (OpOperand &t : linalgOp->getOpOperands()) {
     tensors.push_back(t.get());
-    Level rank = linalgOp.getMatchingIndexingMap(&t).getNumResults();
-    for (Level lvl = 0; lvl < rank; lvl++) {
-      sortArrayBasedOnOrder(
-          latticeMerger.getDependentLoops(t.getOperandNumber(), lvl), topSort);
+    if (getSparseTensorEncoding(t.get().getType())) {
+      Level rank = linalgOp.getMatchingIndexingMap(&t).getNumResults();
+      for (Level lvl = 0; lvl < rank; lvl++) {
+        sortArrayBasedOnOrder(
+            latticeMerger.getDependentLoops(t.getOperandNumber(), lvl),
+            topSort);
+      }
     }
   }
 
@@ -103,11 +106,13 @@
       // passing in a callback.
       [this](TensorId t, Level lvl) -> std::vector<std::pair<TensorId, Level>> {
         // Translates from a list of loop index to a list of [tid, dim] pair.
-        std::vector<LoopId> rLoops = this->merger().getDependentLoops(t, lvl);
         std::vector<std::pair<TensorId, Level>> ret;
-        ret.reserve(rLoops.size());
-        for (LoopId l : rLoops)
-          ret.emplace_back(this->merger().getLoopDefiningLvl(l));
+        if (getSparseTensorEncoding(linalgOp.getOperands()[t].getType())) {
+          std::vector<LoopId> rLoops = this->merger().getDependentLoops(t, lvl);
+          ret.reserve(rLoops.size());
+          for (LoopId l : rLoops)
+            ret.emplace_back(this->merger().getLoopDefiningLvl(l));
+        }
         return ret;
       });
 }
diff --git a/mlir/test/Dialect/SparseTensor/constant_index_map.mlir b/mlir/test/Dialect/SparseTensor/constant_index_map.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Dialect/SparseTensor/constant_index_map.mlir
@@ -0,0 +1,41 @@
+// Reported by https://github.com/llvm/llvm-project/issues/61530
+
+// RUN: mlir-opt %s -sparsification | FileCheck %s
+
+#map1 = affine_map<(d0) -> (0, d0)>
+#map2 = affine_map<(d0) -> (d0)>
+
+#SpVec = #sparse_tensor.encoding<{ dimLevelType = [ "compressed" ] }>
+
+// CHECK-LABEL:   func.func @main(
+// CHECK-SAME:      %[[VAL_0:.*0]]: tensor<1x77xi1>,
+// CHECK-SAME:      %[[VAL_1:.*1]]: tensor<1x77xi1>) -> tensor<77xi1, #{{.*}}> {
+// CHECK-DAG:       %[[VAL_2:.*]] = arith.constant 77 : index
+// CHECK-DAG:       %[[VAL_3:.*]] = arith.constant 0 : index
+// CHECK-DAG:       %[[VAL_4:.*]] = arith.constant 1 : index
+// CHECK-DAG:       %[[VAL_5:.*]] = bufferization.alloc_tensor() : tensor<77xi1, #{{.*}}>
+// CHECK-DAG:       %[[VAL_6:.*]] = bufferization.to_memref %[[VAL_0]] : memref<1x77xi1>
+// CHECK-DAG:       %[[VAL_7:.*]] = bufferization.to_memref %[[VAL_1]] : memref<1x77xi1>
+// CHECK:           %[[VAL_8:.*]] = scf.for %[[VAL_9:.*]] = %[[VAL_3]] to %[[VAL_2]] step %[[VAL_4]] iter_args(%[[VAL_10:.*]] = %[[VAL_5]]) -> (tensor<77xi1, #{{.*}}>) {
+// CHECK:             %[[VAL_11:.*]] = memref.load %[[VAL_6]]{{\[}}%[[VAL_3]], %[[VAL_9]]] : memref<1x77xi1>
+// CHECK:             %[[VAL_12:.*]] = memref.load %[[VAL_7]]{{\[}}%[[VAL_3]], %[[VAL_9]]] : memref<1x77xi1>
+// CHECK:             %[[VAL_13:.*]] = arith.addi %[[VAL_11]], %[[VAL_12]] : i1
+// CHECK:             %[[VAL_14:.*]] = sparse_tensor.insert %[[VAL_13]] into %[[VAL_10]]{{\[}}%[[VAL_9]]] : tensor<77xi1, #{{.*}}>
+// CHECK:             scf.yield %[[VAL_14]] : tensor<77xi1, #{{.*}}>
+// CHECK:           }
+// CHECK:           %[[VAL_15:.*]] = sparse_tensor.load %[[VAL_16:.*]] hasInserts : tensor<77xi1, #{{.*}}>
+// CHECK:           return %[[VAL_15]] : tensor<77xi1, #{{.*}}>
+// CHECK:         }
+func.func @main(%arg0: tensor<1x77xi1>, %arg1: tensor<1x77xi1>) -> tensor<77xi1, #SpVec> {
+  %0 = bufferization.alloc_tensor() : tensor<77xi1, #SpVec>
+  %1 = linalg.generic {
+    indexing_maps = [#map1, #map1, #map2],
+    iterator_types = ["parallel"]}
+    ins(%arg0, %arg1 : tensor<1x77xi1>, tensor<1x77xi1>)
+    outs(%0 : tensor<77xi1, #SpVec>) {
+  ^bb0(%in: i1, %in_0: i1, %out: i1):
+    %2 = arith.addi %in, %in_0 : i1
+    linalg.yield %2 : i1
+  } -> tensor<77xi1, #SpVec>
+  return %1 : tensor<77xi1, #SpVec>
+}
diff --git a/mlir/test/Dialect/SparseTensor/sparse_affine.mlir b/mlir/test/Dialect/SparseTensor/sparse_affine.mlir
--- a/mlir/test/Dialect/SparseTensor/sparse_affine.mlir
+++ b/mlir/test/Dialect/SparseTensor/sparse_affine.mlir
@@ -496,4 +496,3 @@
   } -> tensor<32x16xf64>
   return %0 : tensor<32x16xf64>
 }
-