diff --git a/benchmarks/python/test_transpose.py b/benchmarks/python/test_transpose.py
index 11b66774708..9e91fc0b2f2 100644
--- a/benchmarks/python/test_transpose.py
+++ b/benchmarks/python/test_transpose.py
@@ -15,17 +15,26 @@ def transpose_fusion(
     is_copy_transpose: bool,
     axes: list,
     rank: int,
+    num_inputs: int = 2,
 ):
     shape = [-1] * rank
     contiguity = [True] * rank
     T0 = fd.define_tensor(shape=shape, contiguity=contiguity, dtype=dtype, is_cpu=False)
-    T1 = fd.define_tensor(shape=shape, contiguity=contiguity, dtype=dtype, is_cpu=False)
+
+    if num_inputs == 2:
+        T1 = fd.define_tensor(
+            shape=shape, contiguity=contiguity, dtype=dtype, is_cpu=False
+        )
 
     if dtype in PROMOTE_DTYPES:
         T0 = fd.ops.cast(T0, dtype=DataType.Float)
-        T1 = fd.ops.cast(T1, dtype=DataType.Float)
+        if num_inputs == 2:
+            T1 = fd.ops.cast(T1, dtype=DataType.Float)
 
-    T4 = fd.ops.add(T0, T1)
+    if num_inputs == 2:
+        T4 = fd.ops.add(T0, T1)
+    else:
+        T4 = T0
     T5 = fd.ops.permute(T4, dims=axes)
 
     if dtype in PROMOTE_DTYPES:
@@ -46,11 +55,18 @@ def transpose_fusion(
 # Without contiguous, transpose returns a view with swapped strides.
 # contiguous() materializes a contiguous copy of the result.
 # When compiled with thunder, contiguous version will use nvFuser's transpose scheduler, otherwise it will use the pointwise scheduler.
-def transpose_fwd_fn(inputs: list):  # [input1, input2, dim0, dim1, is_copy_transpose]
-    relu_transpose_result = torch.nn.functional.relu(
-        torch.transpose(inputs[0] + inputs[1], inputs[2], inputs[3])
-    )
-    is_copy_transpose = inputs[4]
+def transpose_fwd_fn(
+    inputs: list,
+):  # [input1, input2 (optional), dim0, dim1, is_copy_transpose, num_inputs]
+    num_inputs = inputs[-1]
+    is_copy_transpose = inputs[-2]
+    if num_inputs == 2:
+        data = inputs[0] + inputs[1]
+        dim0, dim1 = inputs[2], inputs[3]
+    else:
+        data = inputs[0]
+        dim0, dim1 = inputs[1], inputs[2]
+    relu_transpose_result = torch.nn.functional.relu(torch.transpose(data, dim0, dim1))
     if is_copy_transpose:
         return relu_transpose_result.contiguous()
     else:
@@ -75,6 +91,11 @@ def _generate_transpose_params():
     [True, False],
     ids=["copy_transpose", "view_transpose"],
 )
+@pytest.mark.parametrize(
+    "num_inputs",
+    [1, 2],
+    ids=["1_input", "2_inputs"],
+)
 @pytest.mark.pointwise
 def test_transpose_nvf_benchmark(
     benchmark,
@@ -83,11 +104,16 @@ def test_transpose_nvf_benchmark(
     dtype: torch.dtype,
     axes: tuple,
     dims: int,
+    num_inputs: int,
     disable_validation: bool,
     disable_benchmarking: bool,
 ):
     input1 = torch.randn(size, device="cuda", dtype=dtype)
-    input2 = torch.randn(size, device="cuda", dtype=dtype)
+    inputs = [input1]
+    if num_inputs == 2:
+        input2 = torch.randn(size, device="cuda", dtype=dtype)
+        inputs.append(input2)
+
     permute_axes = list(range(len(size)))
     permute_axes[axes[0]], permute_axes[axes[1]] = (
         permute_axes[axes[1]],
@@ -101,16 +127,22 @@ def test_transpose_nvf_benchmark(
             is_copy_transpose,
             permute_axes,
             rank=dims,
+            num_inputs=num_inputs,
         )
 
     if not disable_validation:
-        eager_output = transpose_fwd_fn(
-            [input1, input2, axes[0], axes[1], is_copy_transpose]
-        )
-        fd.validate([input1, input2], [eager_output])
+        if num_inputs == 2:
+            eager_output = transpose_fwd_fn(
+                [input1, input2, axes[0], axes[1], is_copy_transpose, num_inputs]
+            )
+        else:
+            eager_output = transpose_fwd_fn(
+                [input1, axes[0], axes[1], is_copy_transpose, num_inputs]
+            )
+        fd.validate(inputs, [eager_output])
 
     if not disable_benchmarking:
-        run_benchmark(benchmark, fd.execute, [input1, input2])
+        run_benchmark(benchmark, fd.execute, inputs)
 
 
 @pytest.mark.parametrize("executor", DEFAULT_EXECUTORS)
@@ -121,6 +153,11 @@ def test_transpose_nvf_benchmark(
     [True, False],
     ids=["copy_transpose", "view_transpose"],
 )
+@pytest.mark.parametrize(
+    "num_inputs",
+    [1, 2],
+    ids=["1_input", "2_inputs"],
+)
 def test_transpose_baseline_benchmark(
     benchmark,
     size: tuple,
@@ -128,18 +165,26 @@ def test_transpose_baseline_benchmark(
     is_copy_transpose: bool,
     axes: tuple,
     dims: int,
+    num_inputs: int,
     executor: str,
 ):
     if executor == "torchcompile":
         clear_dynamo_cache()
     input1 = torch.randn(size, device="cuda", dtype=dtype)
-    input2 = torch.randn(size, device="cuda", dtype=dtype)
 
     benchmark_fn = with_executor(executor, transpose_fwd_fn)
 
     # Inputs and outputs are same as nvFuser, no need for manual IOByte computation
-    run_benchmark(
-        benchmark,
-        benchmark_fn,
-        [input1, input2, axes[0], axes[1], is_copy_transpose],
-    )
+    if num_inputs == 2:
+        input2 = torch.randn(size, device="cuda", dtype=dtype)
+        run_benchmark(
+            benchmark,
+            benchmark_fn,
+            [input1, input2, axes[0], axes[1], is_copy_transpose, num_inputs],
+        )
+    else:
+        run_benchmark(
+            benchmark,
+            benchmark_fn,
+            [input1, axes[0], axes[1], is_copy_transpose, num_inputs],
+        )
diff --git a/csrc/scheduler/transpose.cpp b/csrc/scheduler/transpose.cpp
index c2511ec5c2f..7f4e5da0634 100644
--- a/csrc/scheduler/transpose.cpp
+++ b/csrc/scheduler/transpose.cpp
@@ -682,6 +682,29 @@ std::unique_ptr<TransposeParams> getTransposeHeuristics(
       "combination of view op with small transpose dimensions are not "
       "supported by transpose scheduler");
 
+  // Double tile_size2 if the default configuration doesn't provide enough
+  // bytes in flight to saturate memory bandwidth. This is based on Little's
+  // law: bytes_in_flight = bandwidth * latency. We estimate the bits in flight
+  // per SM as: (sum of input tensor element sizes) * elements_per_tile *
+  // blocks_per_sm. If this is less than the required bits in flight (derived
+  // from hardware bandwidth and memory latency), we double tile_size2 to
+  // increase the data in flight.
+  const auto dev_prop = at::cuda::getCurrentDeviceProperties();
+  const int64_t max_blocks_per_sm = dev_prop->maxBlocksPerMultiProcessor;
+  const int64_t num_elems_per_tile = tparams->tile_size1 * tparams->tile_size2;
+  const int64_t required_bits_per_sm =
+      scheduler_utils::getRequiredBitsInFlight();
+  int64_t total_input_bits_per_elem = 0;
+  for (auto tv : ir_utils::filterByType<TensorView>(fusion->inputs())) {
+    total_input_bits_per_elem +=
+        dataTypeSizeBit(tv->getDataType().value(), index_type);
+  }
+  const int64_t bits_in_flight_per_sm =
+      total_input_bits_per_elem * num_elems_per_tile * max_blocks_per_sm;
+  if (bits_in_flight_per_sm < required_bits_per_sm) {
+    tparams->tile_size2 *= 2;
+  }
+
   // Note [vectorization and unroll of input and output]
   //
   // The choice of vectorization size, block size and tile sizes needs to be