diff --git a/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp b/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp
--- a/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp
@@ -262,14 +262,24 @@
       break;
     }
   }
-  // Now apply the two basic rules.
+
   BitVector simple = latPoints[p0].bits;
   bool reset = isSingleton && hasAnySparse(simple);
+  unsigned offset = 0;
+  if (!reset)
+    // Starts resetting from a dense dimension, so that the first bit (if kept)
+    // is not undefined dimension type.
+    for (unsigned b = 0, be = simple.size(); b < be; b++)
+      if (simple[b] && isDimLevelType(b, DimLvlType::kDense))
+        offset = b;
+
+  // Now apply the two basic rules.
   for (unsigned b = 0, be = simple.size(); b < be; b++) {
-    if (simple[b] && (!isDimLevelType(b, DimLvlType::kCompressed) &&
-                      !isDimLevelType(b, DimLvlType::kSingleton))) {
+    unsigned i = (offset + b) % simple.size();
+    if (simple[i] && (!isDimLevelType(i, DimLvlType::kCompressed) &&
+                      !isDimLevelType(i, DimLvlType::kSingleton))) {
       if (reset)
-        simple.reset(b);
+        simple.reset(i);
       reset = true;
     }
   }
diff --git a/mlir/unittests/Dialect/SparseTensor/MergerTest.cpp b/mlir/unittests/Dialect/SparseTensor/MergerTest.cpp
--- a/mlir/unittests/Dialect/SparseTensor/MergerTest.cpp
+++ b/mlir/unittests/Dialect/SparseTensor/MergerTest.cpp
@@ -377,8 +377,64 @@
   }
 };
 
+///
+/// Tests with both undef and dense input.
+///
+class MergerTest3T1LU : public MergerTestBase {
+protected:
+  // Our three tensors (two inputs, one output).
+  const unsigned t0 = 0, t1 = 1, t2 = 2;
+
+  // Our single loop.
+  const unsigned l0 = 0;
+
+  MergerTest3T1LU() : MergerTestBase(3, 1) {
+    // Tensor 0: undef input vector.
+    merger.addExp(Kind::kTensor, t0, -1u);
+    merger.setDimLevelFormat(t0, l0, DimLevelFormat(DimLvlType::kUndef));
+
+    // Tensor 1: dense input vector.
+    merger.addExp(Kind::kTensor, t1, -1u);
+    merger.setDimLevelFormat(t1, l0, DimLevelFormat(DimLvlType::kDense));
+
+    // Tensor 2: dense output vector.
+    merger.addExp(Kind::kTensor, t2, -1u);
+    merger.setDimLevelFormat(t2, l0, DimLevelFormat(DimLvlType::kDense));
+  }
+};
 } // namespace
 
+/// Vector multiplication (conjunction) of 2 vectors, i.e.;
+///   a(i) = b(i) * c(i)
+/// which should form the single lattice point
+/// {
+///   lat( i_00_U i_01_D / (tensor_0 * tensor_1) )
+/// }
+/// after optimization, the dense dimesion should be kept, despite it appears
+/// after the undef dimension
+/// {
+///   lat( i_01_D / (tensor_0 * tensor_1) )
+/// }
+#define IMPL_MERGER_TEST_CONJ(OP)                                              \
+  TEST_F(MergerTest3T1LU, vector_##OP) {                                       \
+    auto e = OP##Expr(t0, t1);                                                 \
+    auto p0 = tensorPattern(t0);                                               \
+    auto p1 = tensorPattern(t1);                                               \
+    auto s = merger.buildLattices(e, l0);                                      \
+                                                                               \
+    expectNumLatPoints(s, 1);                                                  \
+    expectLatPoint(s, lat(0), OP##Pattern(p0, p1),                             \
+                   loopsToBits({{l0, t0}, {l0, t1}}));                         \
+                                                                               \
+    s = merger.optimizeSet(s);                                                 \
+    expectNumLatPoints(s, 1);                                                  \
+    expectLatPoint(s, lat(0), OP##Pattern(p0, p1), loopsToBits({{l0, t1}}),    \
+                   true);                                                      \
+  }
+FOREVERY_COMMON_CONJ_BINOP(IMPL_MERGER_TEST_CONJ)
+
+#undef IMPL_MERGER_TEST_CONJ
+
 /// Vector addition (disjunction) of 2 vectors. i.e.;
 ///   a(i) = b(i) + c(i)
 /// which should form the 3 lattice points