diff --git a/transformer_engine/pytorch/cpp_extensions/transpose.py b/transformer_engine/pytorch/cpp_extensions/transpose.py
index 37a1b59da2..ddc3b67e9e 100644
--- a/transformer_engine/pytorch/cpp_extensions/transpose.py
+++ b/transformer_engine/pytorch/cpp_extensions/transpose.py
@@ -175,6 +175,7 @@ def fp8_multi_cast_transpose_fused(
     amax_indices: List[int],
     scale_inv_indices: List[int],
     otype: tex.DType,
+    scale_inv: Optional[torch.Tensor] = None,
 ) -> Tuple[List[torch.Tensor], List[torch.Tensor]]:
     """Cast + Transpose with FP8 output"""
 
@@ -182,7 +183,7 @@ def fp8_multi_cast_transpose_fused(
         input_list,
         fp8_meta_tensor.scale,
         fp8_meta_tensor.amax_history,
-        fp8_meta_tensor.scale_inv,
+        scale_inv if scale_inv is not None else fp8_meta_tensor.scale_inv,
         scale_indices,
         amax_indices,
         scale_inv_indices,
diff --git a/transformer_engine/pytorch/module/grouped_linear.py b/transformer_engine/pytorch/module/grouped_linear.py
index a91ff5c361..7f56ced8ef 100644
--- a/transformer_engine/pytorch/module/grouped_linear.py
+++ b/transformer_engine/pytorch/module/grouped_linear.py
@@ -42,6 +42,7 @@
 from ..jit import no_torch_dynamo
 from ..graph import is_graph_capturing
 from ..float8_tensor import Float8Tensor
+from ..export import is_in_onnx_export_mode
 
 __all__ = ["GroupedLinear"]
 
@@ -102,10 +103,12 @@ def forward(
         inputmats_no_fp8 = [cast_if_needed(mat, activation_dtype) for mat in inputmats]
         inputmats = []
         inputmats_t = []
+        inputmat_scale_inv = None
 
         global _GEMM_INPUT, _GEMM_WEIGHT, _GEMM_OUTPUT
         if fp8:
             fp8_dtype_forward = get_fp8_te_dtype(fp8_meta["recipe"], fprop_tensor=True)
+            inputmat_scale_inv = torch.empty([num_gemms], dtype=torch.float32, device=inp.device)
             if (
                 not fp8_meta["recipe"].override_linear_precision.wgrad
                 and is_grad_enabled
@@ -121,6 +124,7 @@ def forward(
                     indices,  # amax_indices
                     indices,  # scale_inv_indices
                     fp8_dtype_forward,
+                    scale_inv=inputmat_scale_inv,
                 )
             else:
                 # FP8 input for forward
@@ -130,9 +134,22 @@ def forward(
                         fp8_meta["scaling_fwd"],
                         _GEMM_INPUT + i,
                         fp8_dtype_forward,
+                        scale_inv=inputmat_scale_inv,
                     )
                     for i in range(num_gemms)
                 ]
+
+            # Hack for ONNX export
+            # Note: ONNX models are represented as a graph of tensor
+            # operations, so the in-place scale-inv update doesn't fit
+            # very well. We work around this by making it look like
+            # the scale-inv tensor is initialized with a copy.
+            # Note: ONNX export expects FP8 scales can be represented
+            # with constant ops. However, copying into a buffer
+            # involves an expand op for array broadcasting. We work
+            # around this by filling the buffer instead.
+            if is_in_onnx_export_mode():
+                inputmat_scale_inv.fill_(inputmat_scale_inv.item())
         else:
             inputmats = inputmats_no_fp8
 
@@ -153,12 +170,14 @@ def forward(
 
             _ = fp8_grouped_gemm(
                 [w._data for w in weights_fp8],
-                fp8_meta["scaling_fwd"].scale_inv,
-                _GEMM_WEIGHT,
+                torch.cat(
+                    [w._scale_inv for w in weights_fp8]
+                ),  # avoiding torch.cat requires another interface,
+                0,  # weight offset is 0 for the newly created _scale_inv
                 fp8_dtype_forward,
                 inputmats,
-                fp8_meta["scaling_fwd"].scale_inv,
-                _GEMM_INPUT,
+                inputmat_scale_inv,
+                0,
                 fp8_dtype_forward,
                 torch.split(out, m_splits),
                 activation_dtype,
@@ -230,7 +249,7 @@ def forward(
                             t.activation_offloading = True
 
             ctx.save_for_backward(
-                fp8_meta["scaling_fwd"].scale_inv.clone() if fp8 else None,
+                inputmat_scale_inv,
                 *saved_inputmats,
                 *saved_inputmats_t,
                 *weights,
@@ -270,7 +289,7 @@ def forward(
     def backward(ctx, grad_output: torch.Tensor) -> Tuple[Union[torch.Tensor, None], ...]:
         with torch.cuda.nvtx.range("_GroupedLinear_backward"):
             (
-                fwd_scale_inverses,
+                inputmat_scale_inv,
                 *saved_tensors,
             ) = ctx.saved_tensors
             inputmats = saved_tensors[: ctx.num_gemms]
@@ -396,8 +415,8 @@ def backward(ctx, grad_output: torch.Tensor) -> Tuple[Union[torch.Tensor, None],
                                 inp._data if isinstance(inp, Float8Tensor) else inp
                                 for inp in inputmats_t
                             ],
-                            fwd_scale_inverses,
-                            _GEMM_INPUT,
+                            inputmat_scale_inv,
+                            0,
                             fp8_dtype_forward,
                             grad_output_t,
                             ctx.fp8_meta["scaling_bwd"].scale_inv,