diff --git a/src/schedule/message_passing.cc b/src/schedule/message_passing.cc
index 12c5db703ec58..34e756d369ef1 100644
--- a/src/schedule/message_passing.cc
+++ b/src/schedule/message_passing.cc
@@ -270,10 +270,24 @@ void PassUpDomain(const FuseNode* s,
     *outer = IntSet::single_point(v_outer);
     *inner = IntSet::single_point(v_inner);
   } else {
-    LOG(WARNING) << "use fallback inference rule in fuse";
-    // simply use the entire set, this rule can be enhanced.
-    *outer = IntSet::range(dom_map.at(s->outer));
-    *inner = IntSet::range(dom_map.at(s->inner));
+    Expr fused_extent = (fused.max() - fused.min() + 1);
+    Expr inner_extent = dom_map.at(s->inner)->extent;
+    *outer = IntSet::interval(outer_min + fused.min() / inner_extent,
+            outer_min + fused.max() / inner_extent);
+    if ( is_zero(Simplify(inner_extent % fused_extent)) &&
+      is_zero(Simplify(fused.min() % fused_extent)) ) {
+      // fused never spans multiple rows, make a tight bounding box
+      // there may be other cases when bounding box could be tightened
+      *inner = IntSet::interval(inner_min + fused.min() % inner_extent,
+                                inner_min + fused.max() % inner_extent);
+    } else {  // fused may span multiple rows, use full row widths
+      if (!is_zero(Simplify(fused_extent % inner_extent)) ||
+        !is_zero(Simplify(fused.min() % inner_extent))) {
+        LOG(WARNING) <<
+          "fused and original axes are not aligned, this may cause redundant computations";
+      }
+      *inner = IntSet::range(dom_map.at(s->inner));
+    }
     return;
   }
 }
diff --git a/tests/python/unittest/test_schedule_bound_inference.py b/tests/python/unittest/test_schedule_bound_inference.py
index f16305779a43a..740527116a6e5 100644
--- a/tests/python/unittest/test_schedule_bound_inference.py
+++ b/tests/python/unittest/test_schedule_bound_inference.py
@@ -69,6 +69,55 @@ def test_bound3():
     assert(bounds[A1.op.axis[0]].extent.value==32)
     assert(bounds[A1.op.axis[1]].extent.value==16)
 
+def test_bound_fusesplit1():
+    m = tvm.var('m')
+    l = tvm.var('l')
+    split1 = tvm.var('s')
+    A = tvm.placeholder((m, l), name='A')
+    A1 = tvm.compute((m, l), lambda i, j: A[i, j], name='A1')
+    A2 = tvm.compute((m, l), lambda i, j: A1[i, j] + 3, name='A2')
+
+    s = tvm.create_schedule(A2.op)
+    fused_axes = s[A2].fuse(A2.op.axis[0], A2.op.axis[1])
+    xo, xi = s[A2].split(fused_axes, split1)
+    s[A1].compute_at(s[A2], xo)
+
+    bounds = tvm.schedule.InferBound(s)
+    assert isinstance(bounds, tvm.container.Map)
+    assert(tvm.ir_pass.Simplify(bounds[A1.op.axis[0]].min - (xo * split1) / l ).value == 0)
+
+    expected_extent = (((xo + 1) * split1 - 1) / l - (xo * split1) / l + 1)
+    for i in range(1, 6):
+        for j in range(1, 6):
+            for k in range(1, 6):
+                vars = tvm.convert({split1: tvm.const(i, "int32"), l: tvm.const(j, "int32"), xo.var: tvm.const(k, "int32")})
+                comp_ext = tvm.ir_pass.Simplify(tvm.ir_pass.Substitute(bounds[A1.op.axis[0]].extent, vars)).value
+                exp_ext = tvm.ir_pass.Simplify(tvm.ir_pass.Substitute(expected_extent, vars)).value
+                assert( comp_ext == exp_ext )
+    
+    assert(tvm.ir_pass.Simplify(bounds[A1.op.axis[1]].extent - l).value == 0)
+
+def test_bound_fusesplit2():
+    m = tvm.var("m")
+    l = tvm.convert(6)
+    split = tvm.convert(3)
+    A = tvm.placeholder((m, l), name='A')
+    A1 = tvm.compute((m, l), lambda i, j: A[i, j], name='A1')
+    A2 = tvm.compute((m, l), lambda i, j: A1[i, j] + 3, name='A2')
+
+    s = tvm.create_schedule(A2.op)
+    fused_axes = s[A2].fuse(A2.op.axis[0], A2.op.axis[1])
+    xo, xi = s[A2].split(fused_axes, split)
+    s[A1].compute_at(s[A2], xo)
+
+    bounds = tvm.schedule.InferBound(s)
+    assert isinstance(bounds, tvm.container.Map)
+    vars = tvm.convert({xo.var: tvm.const(5, "int32")})
+    assert(tvm.ir_pass.Simplify(tvm.ir_pass.Substitute(bounds[A1.op.axis[0]].min, vars)).value == 2)
+    assert(tvm.ir_pass.Simplify(tvm.ir_pass.Substitute(bounds[A1.op.axis[1]].min, vars)).value == 3)
+    assert(tvm.ir_pass.Simplify(tvm.ir_pass.Substitute(bounds[A1.op.axis[0]].extent, vars)).value == 1)
+    assert(tvm.ir_pass.Simplify(tvm.ir_pass.Substitute(bounds[A1.op.axis[1]].extent, vars)).value == 3)
+
 
 def test_bound_warp():
     m = tvm.var('m')
@@ -320,3 +369,5 @@ def _body():
     test_gemm_bound()
     test_bound_warp()
     test_bound_tensor_compute_op()
+    test_bound_fusesplit1()
+    test_bound_fusesplit2()