diff --git a/mlir/lib/Transforms/LoopFusion.cpp b/mlir/lib/Transforms/LoopFusion.cpp
--- a/mlir/lib/Transforms/LoopFusion.cpp
+++ b/mlir/lib/Transforms/LoopFusion.cpp
@@ -921,21 +921,17 @@
   // Build an AffineMap to remap access functions based on lower bound offsets.
   SmallVector<AffineExpr, 4> remapExprs;
   remapExprs.reserve(rank);
-  unsigned zeroOffsetCount = 0;
   for (unsigned i = 0; i < rank; i++) {
-    if (auto constExpr = offsets[i].dyn_cast<AffineConstantExpr>())
-      if (constExpr.getValue() == 0)
-        ++zeroOffsetCount;
     auto dimExpr = b.getAffineDimExpr(outerIVs.size() + i);
 
     auto remapExpr =
         simplifyAffineExpr(dimExpr - offsets[i], outerIVs.size() + rank, 0);
     remapExprs.push_back(remapExpr);
   }
-  auto indexRemap = zeroOffsetCount == rank
-                        ? AffineMap()
-                        : AffineMap::get(outerIVs.size() + rank, 0, remapExprs,
-                                         forOp.getContext());
+
+  auto indexRemap =
+      AffineMap::get(outerIVs.size() + rank, 0, remapExprs, forOp.getContext());
+
   // Replace all users of 'oldMemRef' with 'newMemRef'.
   LogicalResult res =
       replaceAllMemRefUsesWith(oldMemRef, newMemRef, {}, indexRemap,
diff --git a/mlir/test/Transforms/loop-fusion.mlir b/mlir/test/Transforms/loop-fusion.mlir
--- a/mlir/test/Transforms/loop-fusion.mlir
+++ b/mlir/test/Transforms/loop-fusion.mlir
@@ -2634,3 +2634,32 @@
 // CHECK:  affine.for
 // CHECK:    mulf
 // CHECK:    subf
+
+// -----
+
+// MAXIMAL-LABEL: func @fuse_minor_affine_map
+func @fuse_minor_affine_map(%in: memref<128xf32>, %out: memref<20x512xf32>) {
+  %tmp = alloc() : memref<128xf32>
+
+  affine.for %arg4 = 0 to 128 {
+    %ld = affine.load %in[%arg4] : memref<128xf32>
+    affine.store %ld, %tmp[%arg4] : memref<128xf32>
+  }
+
+  affine.for %arg3 = 0 to 20 {
+    affine.for %arg4 = 0 to 512 {
+      %ld = affine.load %tmp[%arg4 mod 128] : memref<128xf32>
+      affine.store %ld, %out[%arg3, %arg4] : memref<20x512xf32>
+    }
+  }
+
+  return
+}
+
+// TODO: The size of the private memref is not properly computed in the presence
+// of the 'mod' operation. It should be memref<1xf32> instead of
+// memref<128xf32>: https://bugs.llvm.org/show_bug.cgi?id=46973
+// MAXIMAL:       alloc() : memref<128xf32>
+// MAXIMAL:       affine.for
+// MAXIMAL-NEXT:    affine.for
+// MAXIMAL-NOT:   affine.for