diff --git a/src/arith/iter_affine_map.cc b/src/arith/iter_affine_map.cc
index c76729c4ef26..519a05412b73 100644
--- a/src/arith/iter_affine_map.cc
+++ b/src/arith/iter_affine_map.cc
@@ -2175,10 +2175,16 @@ ffi::Array<PrimExpr> IterMapSimplify(const ffi::Array<PrimExpr>& indices,
   if (rewrite.empty() && !is_one(input_pred) && check_level != IterMapLevel::Bijective) {
     // The input predicate may cause detect iter map to fail
     // but we can still detect the iter map without the input predicate
-    // in which case the resulting iter map is valid and can be used for simplification.
-    rewrite = DetectIterMap(indices, input_iters, IntImm::Bool(true), check_level, ana,
-                            /*simplify_trivial_iterators=*/simplify_trivial_iterators)
-                  ->indices;
+    // in which case an unpadded iter map is valid and can be used for
+    // simplification.
+    auto fallback = DetectIterMap(indices, input_iters, IntImm::Bool(true), check_level, ana,
+                                  /*simplify_trivial_iterators=*/simplify_trivial_iterators);
+    // A padded fallback is not equivalent over the original iterator domain unless its
+    // padding predicate is also preserved.  IterMapSimplify only returns expressions, so it
+    // cannot carry that predicate to callers.
+    if (!fallback->indices.empty() && is_zero(fallback->padding_predicate)) {
+      rewrite = fallback->indices;
+    }
   }
 
   if (rewrite.empty()) {
diff --git a/tests/python/arith/test_arith_iter_affine_map.py b/tests/python/arith/test_arith_iter_affine_map.py
index 375760118b5f..e3cb75749ec6 100644
--- a/tests/python/arith/test_arith_iter_affine_map.py
+++ b/tests/python/arith/test_arith_iter_affine_map.py
@@ -1234,6 +1234,33 @@ def fsymbolic_fuse2(i):
     )
 
 
+def test_iter_map_simplify_predicate_fallback_requires_no_padding():
+    fused = tvm.tirx.Var("fused", "int64")
+    predicate = fused % 2 == 0
+    unpadded_index = fused // 4 * 4 + fused % 4
+    simplified = tvm.arith.iter_map_simplify(
+        [unpadded_index],
+        var_dom([(fused, 1024)]),
+        predicate=predicate,
+    )
+    tvm.ir.assert_structural_equal(simplified, [fused])
+
+    kernel = tvm.tirx.Var("kernel", "int64")
+    value = fused % 14 + kernel
+    index = (value - 1) // 2
+    predicate = (value + 1) % 2 == 0
+
+    # The parity predicate is not a bound constraint, so IterMapSimplify falls back to
+    # detecting the map without it.  That fallback requires left-padding the iterator;
+    # discarding the corresponding padding predicate would change the index expression.
+    simplified = tvm.arith.iter_map_simplify(
+        [index],
+        var_dom([(fused, 1024), (kernel, 3)]),
+        predicate=predicate,
+    )
+    tvm.ir.assert_structural_equal(simplified, [index])
+
+
 def test_iter_map_simplify_symbolic_reshape():
     n = tvm.tirx.Var("n", "int64")
     fused = tvm.tirx.Var("fused", "int64")