diff --git a/src/timesfm/flax/util.py b/src/timesfm/flax/util.py
index ec70d724..ef792e99 100644
--- a/src/timesfm/flax/util.py
+++ b/src/timesfm/flax/util.py
@@ -101,7 +101,8 @@ def revin(
   elif len(mu.shape) == len(x.shape) - 2:
     mu = mu[..., None, None]
     sigma = sigma[..., None, None]
+  safe_sigma = jnp.where(sigma < _TOLERANCE, 1.0, sigma)
   if reverse:
-    return x * sigma + mu
+    return x * safe_sigma + mu
   else:
-    return (x - mu) / jnp.where(sigma < _TOLERANCE, 1.0, sigma)
+    return (x - mu) / safe_sigma
diff --git a/src/timesfm/torch/util.py b/src/timesfm/torch/util.py
index 81efe292..2bdf8eb4 100644
--- a/src/timesfm/torch/util.py
+++ b/src/timesfm/torch/util.py
@@ -88,7 +88,8 @@ def revin(
     mu = mu[..., None, None]
     sigma = sigma[..., None, None]
 
+  safe_sigma = torch.where(sigma < _TOLERANCE, 1.0, sigma)
   if reverse:
-    return x * sigma + mu
+    return x * safe_sigma + mu
   else:
-    return (x - mu) / torch.where(sigma < _TOLERANCE, 1.0, sigma)
+    return (x - mu) / safe_sigma
diff --git a/src/timesfm3/mlx/util.py b/src/timesfm3/mlx/util.py
index 1b87ea96..f0e36771 100644
--- a/src/timesfm3/mlx/util.py
+++ b/src/timesfm3/mlx/util.py
@@ -47,9 +47,9 @@ def revin(
     mu, sigma = mu[..., None], sigma[..., None]
   elif mu.ndim == x.ndim - 2:
     mu, sigma = mu[..., None, None], sigma[..., None, None]
-  if reverse:
-    return x * sigma + mu
   safe_sigma = mx.where(sigma < DIV_TOL, 1.0, sigma)
+  if reverse:
+    return x * safe_sigma + mu
   return (x - mu) / safe_sigma
 
 
diff --git a/src/timesfm3/torch/primitives_test.py b/src/timesfm3/torch/primitives_test.py
index 7d3a2f5b..cc4e471a 100644
--- a/src/timesfm3/torch/primitives_test.py
+++ b/src/timesfm3/torch/primitives_test.py
@@ -287,6 +287,22 @@ def test_revin_near_zero_sigma(self):
     expected = torch.tensor([[[0.0, 0.0, 0.0]]])
     np.testing.assert_allclose(normalized_x.numpy(), expected.numpy(), atol=1e-6)
 
+  def test_revin_zero_sigma_roundtrip(self):
+    x = torch.tensor([[[4.5, 5.0, 5.5]]])
+    mu = torch.tensor([[5.0]])
+    sigma = torch.tensor([[0.0]])
+    normalized_x = torch_util.revin(x, mu, sigma, reverse=False)
+    recovered_x = torch_util.revin(normalized_x, mu, sigma, reverse=True)
+    np.testing.assert_allclose(recovered_x.numpy(), x.numpy(), atol=1e-5)
+
+  def test_revin_near_zero_sigma_roundtrip(self):
+    x = torch.tensor([[[1.0, 2.0, 3.0]]])
+    mu = torch.tensor([[2.0]])
+    sigma = torch.tensor([[1e-7]])
+    normalized_x = torch_util.revin(x, mu, sigma, reverse=False)
+    recovered_x = torch_util.revin(normalized_x, mu, sigma, reverse=True)
+    np.testing.assert_allclose(recovered_x.numpy(), x.numpy(), atol=1e-5)
+
   def test_get_output_patch_via_roll(self):
     x = torch.tensor([[[[1, 2], [3, 4], [5, 6], [7, 8]]]], dtype=torch.float32)
     rolls = 2
diff --git a/src/timesfm3/torch/util.py b/src/timesfm3/torch/util.py
index 06350ba6..f482e216 100644
--- a/src/timesfm3/torch/util.py
+++ b/src/timesfm3/torch/util.py
@@ -251,10 +251,11 @@ def revin(
     sigma = sigma.unsqueeze(-1).unsqueeze(-1)
   else:
     raise ValueError(f"Unsupported shapes for x and mu: {x.shape}, {mu.shape}.")
+  safe_sigma = _make_safe_for_division(sigma)
   if reverse:
-    return x * sigma + mu
+    return x * safe_sigma + mu
   else:
-    return (x - mu) / _make_safe_for_division(sigma)
+    return (x - mu) / safe_sigma
 
 
 def get_output_patch_via_roll(
diff --git a/tests/test_torch_utils.py b/tests/test_torch_utils.py
index 76f2296a..bb674e72 100644
--- a/tests/test_torch_utils.py
+++ b/tests/test_torch_utils.py
@@ -254,6 +254,33 @@ def test_near_zero_sigma_guarded_by_tolerance(self):
     expected = torch.tensor([[-1.0, 0.0, 1.0]])
     torch.testing.assert_close(normed, expected, atol=1e-5, rtol=1e-5)
 
+  def test_zero_sigma_roundtrip_identity(self):
+    """Zero variance must reconstruct the original input in roundtrip.
+
+    When sigma is zero, forward normalization guards division by using
+    effective scale 1.0. Reverse denormalization must symmetrically use the
+    same effective scale 1.0 to preserve forecast deltas.
+    """
+    x = torch.tensor([[4.5, 5.0, 5.5]])
+    mu = torch.tensor([5.0])
+    sigma = torch.tensor([0.0])
+
+    normed = revin(x, mu, sigma, reverse=False)
+    recovered = revin(normed, mu, sigma, reverse=True)
+
+    torch.testing.assert_close(recovered, x, atol=1e-5, rtol=1e-5)
+
+  def test_near_zero_sigma_roundtrip_identity(self):
+    """Near-zero variance below tolerance must reconstruct original input in roundtrip."""
+    x = torch.tensor([[1.0, 2.0, 3.0]])
+    mu = torch.tensor([2.0])
+    sigma = torch.tensor([_TOLERANCE / 2])
+
+    normed = revin(x, mu, sigma, reverse=False)
+    recovered = revin(normed, mu, sigma, reverse=True)
+
+    torch.testing.assert_close(recovered, x, atol=1e-5, rtol=1e-5)
+
   def test_roundtrip_with_batched_3d_input(self):
     """RevIN must broadcast correctly for (batch, patches, patch_len)
     tensors — the actual shape used during patched decoding."""