diff --git a/CHANGELOG.md b/CHANGELOG.md
index fe66d2136..8de738230 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -21,6 +21,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Fixed
 
+- Fixed unscaled `pred_std` when `output_std=True` in `BaseGraphModel` which caused exponential loss blowup during probabilistic model training [\#347](https://github.com/mllam/neural-lam/issues/347)
 - Initialize `da_forcing_mean` and `da_forcing_std` to `None` when forcing data is absent, fixing `AttributeError` in `WeatherDataset` with `standardize=True` [\#369](https://github.com/mllam/neural-lam/issues/369) @Sir-Sloth-The-Lazy
 
 - Ensure proper sorting of `analysis_time` in `NpyFilesDatastoreMEPS._get_analysis_times` independent of the order in which files are processed with glob [\#386](https://github.com/mllam/neural-lam/pull/386) @Gopisokk
diff --git a/neural_lam/models/base_graph_model.py b/neural_lam/models/base_graph_model.py
index fd38a2e67..6261d494f 100644
--- a/neural_lam/models/base_graph_model.py
+++ b/neural_lam/models/base_graph_model.py
@@ -348,10 +348,10 @@ def predict_step(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.
             # 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