diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3ee3166b..1260de5e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -64,6 +64,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 - Log every figure passed to `CustomMLFlowLogger.log_image` instead of silently dropping all but the first, using per-figure indexed keys (`{key}_{i}`) when more than one is supplied [\#499](https://github.com/mllam/neural-lam/pull/499) @Raj-Taware
 
+- Scale predicted `pred_std` by `self.diff_std` in `output_std=True` graph step-predictors so it starts on the empirical one-step difference scale, avoiding early-training NLL/CRPS blow-up for variables whose physical step-diff std is much larger than `softplus(0) = ln(2)` ([#347](https://github.com/mllam/neural-lam/issues/347)) [\#523](https://github.com/mllam/neural-lam/pull/523) @Debadri-das
+
 ### Maintenance
 
 - Add comprehensive type hints to `neural_lam/metrics.py` [\#447](https://github.com/mllam/neural-lam/pull/447) @sidhantpande
diff --git a/neural_lam/models/step_predictors/graph/base.py b/neural_lam/models/step_predictors/graph/base.py
index 4522d307..82263082 100644
--- a/neural_lam/models/step_predictors/graph/base.py
+++ b/neural_lam/models/step_predictors/graph/base.py
@@ -272,10 +272,17 @@ def forward(self, prev_state, prev_prev_state, forcing):
             pred_delta_mean, pred_std_raw = net_output.chunk(
                 2, dim=-1
             )  # both (B, num_grid_nodes, d_f)
-            # NOTE: The predicted std. is not scaled in any way here
+            # Scale predicted std. with one-step difference std. so that
+            # the initial pred_std is on the empirical scale of the data,
+            # mirroring the diff_std scaling of pred_delta_mean below.
+            # Without this, NLL/CRPS explode in early training for
+            # variables whose physical step-diff std is much greater than
+            # softplus(0) = ln(2).
             # linter for some reason does not think softplus is callable
             # pylint: disable-next=not-callable
-            pred_std = torch.nn.functional.softplus(pred_std_raw)
+            pred_std = (
+                torch.nn.functional.softplus(pred_std_raw) * self.diff_std
+            )
         else:
             pred_delta_mean = net_output
             pred_std = None