diff --git a/qa/L0_pytorch_unittest/test.sh b/qa/L0_pytorch_unittest/test.sh
index ded45dd377..2c14664dce 100644
--- a/qa/L0_pytorch_unittest/test.sh
+++ b/qa/L0_pytorch_unittest/test.sh
@@ -8,6 +8,7 @@ set -e
 
 pip install pytest==7.2 onnxruntime==1.13.1
 pytest -v -s $TE_PATH/tests/pytorch/test_sanity.py
+pytest -v -s $TE_PATH/tests/pytorch/test_recipe.py
 pytest -v -s $TE_PATH/tests/pytorch/test_deferred_init.py
 PYTORCH_JIT=0 NVTE_TORCH_COMPILE=0 NVTE_ALLOW_NONDETERMINISTIC_ALGO=0 pytest -v -s $TE_PATH/tests/pytorch/test_numerics.py
 PYTORCH_JIT=0 NVTE_TORCH_COMPILE=0 NVTE_ALLOW_NONDETERMINISTIC_ALGO=0 pytest -v -s $TE_PATH/tests/pytorch/test_cuda_graphs.py
diff --git a/tests/pytorch/test_recipe.py b/tests/pytorch/test_recipe.py
index 6b65960ec6..92c7f26f59 100644
--- a/tests/pytorch/test_recipe.py
+++ b/tests/pytorch/test_recipe.py
@@ -9,9 +9,10 @@
 
 import transformer_engine.common.recipe
 import transformer_engine.pytorch as te
+import transformer_engine_extensions as tex
 from transformer_engine.pytorch.fp8 import (
     FP8GlobalStateManager,
-    amax_and_scale_update,
+    _amax_and_scale_update,
     get_default_fp8_recipe,
 )
 
@@ -162,3 +163,98 @@ def test_amax_and_scale_update(
             fp8_meta[backward_key].scale_inv,
             ref_scale_inv_backward,
         )
+
+    @pytest.mark.parametrize("amax_case", ["zero", "tiny", "normal", "inf", "nan"])
+    @pytest.mark.parametrize("fused_update", [True, False], ids=["fused", "non-fused"])
+    @pytest.mark.parametrize(
+        "fp8_dtype", [tex.DType.kFloat8E4M3, tex.DType.kFloat8E5M2], ids=["E4M3", "E5M2"]
+    )
+    def test_scale_update_numeric_scenarios(self, amax_case, fused_update, fp8_dtype):
+
+        if fp8_dtype == tex.DType.kFloat8E4M3:
+            fp8_format = transformer_engine.common.recipe.Format.E4M3
+            fp8_max = fp8_format.value.max_fwd
+        elif fp8_dtype == tex.DType.kFloat8E5M2:
+            fp8_format = transformer_engine.common.recipe.Format.HYBRID
+            fp8_max = fp8_format.value.max_bwd
+        else:
+            raise ValueError(f"{fp8_dtype=} is not supported")
+
+        scaling_factor_compute_algo = None
+        if fused_update:
+            scaling_factor_compute_algo = (
+                lambda amax, scale, fp8_max, recipe:
+                te.fp8._default_sf_compute(amax, scale, fp8_max, recipe.margin)
+            )
+        recipe = transformer_engine.common.recipe.DelayedScaling(
+            fp8_format=fp8_format, scaling_factor_compute_algo=scaling_factor_compute_algo
+        )
+
+        # Setup fp8_meta dictionary
+        def setup_fp8_meta():
+            with te.fp8_autocast(enabled=True, fp8_recipe=recipe):
+                module = te.Linear(16, 16)
+                y = module(torch.zeros([16, 16], device="cuda"))
+            y.backward(torch.zeros_like(y))
+            return module.fp8_meta
+
+        fp8_meta = setup_fp8_meta()
+        forward_key = FP8GlobalStateManager.get_meta_tensor_key(forward=True)
+
+        # Replace the fp8_meta[forward_key] with a new TensorMeta for test purpose
+        fp8_meta[forward_key] = tex.FP8TensorMeta()
+        fp8_meta[forward_key].scale = torch.ones(1, dtype=torch.float32, device="cuda")
+        fp8_meta[forward_key].scale_inv = torch.ones(1, dtype=torch.float32, device="cuda")
+
+        # test different scenarios
+        if amax_case == "zero":
+            fp8_meta[forward_key].amax_history = torch.tensor([[0]], dtype=torch.float32, device="cuda")
+            expected_scale = torch.tensor([1.0], dtype=torch.float32, device="cuda")
+        elif amax_case == "tiny":
+            # calculate the minimum amax value that results in a FP32 maximum scale
+            fp32_max = torch.tensor(torch.finfo(torch.float32).max)
+            tiny_amax = fp8_max / fp32_max
+            # make the amax less than the minimum amax so that the scale will be infinite
+            amax_value = tiny_amax / 2
+            fp8_meta[forward_key].amax_history = torch.tensor(
+                [[amax_value]], dtype=torch.float32, device="cuda"
+            )
+            # expected scale is FP32_max
+            expected_scale = fp32_max.view(1).cuda()
+        elif amax_case == "normal":
+            # plus a small epsilon to avoid zero amax
+            amax_value = torch.rand(1, dtype=torch.float32, device="cuda") + 1e-5
+            fp8_meta[forward_key].amax_history = amax_value.view(1, 1)
+            expected_scale = fp8_max / amax_value
+        elif amax_case == "inf":
+            fp8_meta[forward_key].amax_history = torch.tensor(
+                [[torch.inf]], dtype=torch.float32, device="cuda"
+            )
+            expected_scale = torch.tensor([1.0], dtype=torch.float32, device="cuda")
+        elif amax_case == "nan":
+            fp8_meta[forward_key].amax_history = torch.tensor(
+                [[torch.nan]], dtype=torch.float32, device="cuda"
+            )
+            expected_scale = torch.tensor([1.0], dtype=torch.float32, device="cuda")
+
+        if fused_update:
+            tex.fused_amax_and_scale_update_after_reduction(
+                fp8_meta[forward_key].amax_history.clone().view(-1),
+                [fp8_meta[forward_key].amax_history],
+                [fp8_meta[forward_key].scale],
+                [fp8_meta[forward_key].scale_inv],
+                recipe.amax_compute_algo,
+                fp8_dtype,
+                recipe.margin,
+            )
+        else:
+            _amax_and_scale_update(
+                fp8_meta[forward_key].amax_history,
+                fp8_meta[forward_key].scale,
+                fp8_meta[forward_key].scale_inv,
+                fp8_max,
+                recipe,
+            )
+
+        torch.testing.assert_close(fp8_meta[forward_key].scale, expected_scale)
+        torch.testing.assert_close(fp8_meta[forward_key].scale_inv, torch.reciprocal(expected_scale))
diff --git a/transformer_engine/common/recipe/delayed_scaling.cu b/transformer_engine/common/recipe/delayed_scaling.cu
index de48a53ebf..2e232f50e2 100644
--- a/transformer_engine/common/recipe/delayed_scaling.cu
+++ b/transformer_engine/common/recipe/delayed_scaling.cu
@@ -8,6 +8,7 @@
 
 #include <cmath>
 #include <string>
+#include <limits>
 
 #include "../common.h"
 #include "../util/logging.h"
@@ -151,6 +152,13 @@ kernel(const float* amax_history_ptr,
     } else {
       scale = scale_ptr[bid];
     }
+    // When the amax is too tiny that the scale becoming infinite in FP32,
+    // we set the scale to the max value of FP32. In this case, the tensor’s
+    // amax won't get mapped to the FP8 max representable, but rather
+    // something below that, but this is the best thing we can do.
+    if (isinf(scale)) {
+        scale = std::numeric_limits<float>::max();
+    }
     updated_scale_ptr[bid] = scale;
 
     // Update scale inverse
@@ -239,12 +247,30 @@ kernel_bulk(
 
     // Update scale and scale inverse
     if (tid == 0) {
+      // Computing the scaling factor requires consideration of the following scenarios:
+      // 1. amax == 0:
+      //    No action is possible, set scale to the previous scale (or 1).
+      // 2. 0 < amax < tiny_amax
+      //    The amax is too tiny that the scale becomes infinite in FP32.
+      //    Set scale = FP32_max
+      // 3. tiny_amax <= amax < FP32_max:
+      //    Set scale = FP8_max (or scaled_max) / amax
+      // 4. When amax == inf or amax == nan:
+      //    No action is possible, set scale to the previous scale (or 1).
+
       float scale;
       if (isfinite(amax) && amax > 0) {
         scale = scaled_max / amax;
       } else {
         scale = p.param[bid].scale[count];
       }
+      // When the amax is too tiny that the scale becoming infinite in FP32,
+      // we set the scale to the max value of FP32. In this case, the tensor’s
+      // amax won't get mapped to the FP8 max representable, but rather
+      // something below that, but this is the best thing we can do.
+      if (isinf(scale)) {
+          scale = std::numeric_limits<float>::max();
+      }
       p.param[bid].scale[count] = scale;
       p.param[bid].scale_inv[count] = 1 / scale;
     }
diff --git a/transformer_engine/pytorch/fp8.py b/transformer_engine/pytorch/fp8.py
index 1f359d4864..b28e380473 100644
--- a/transformer_engine/pytorch/fp8.py
+++ b/transformer_engine/pytorch/fp8.py
@@ -598,11 +598,24 @@ def _default_sf_compute(
     scale: torch.Tensor,
     fp8_max: float,
     margin: int,
+    _fp32_max: float = torch.finfo(torch.float32).max,  # finfo not available in jitter
 ) -> torch.Tensor:
-    """Default function to convert amax to scaling factor."""
+    """Default function to convert amax to scaling factor.
+    Computing the scaling factor requires consideration of the following scenarios:
+    1. amax == 0:
+       No action is possible, set scale to the previous scale (or 1).
+    2. 0 < amax < tiny_amax
+       The amax is too tiny that the scale becomes infinite in FP32.
+       Set scale = FP32_max
+    3. tiny_amax <= amax < FP32_max:
+       Set scale = FP8_max (or scaled_max) / amax
+    4. When amax == inf or amax == nan:
+       No action is possible, set scale to the previous scale (or 1).
+    """
     sf = (fp8_max / amax) / (2 ** margin)
     sf = torch.where(amax > 0.0, sf, scale)
     sf = torch.where(torch.isfinite(amax), sf, scale)
+    sf = torch.where(torch.isinf(sf), torch.full_like(sf, _fp32_max), sf)
     scale.copy_(sf)
     return scale