diff --git a/sbi/utils/sbiutils.py b/sbi/utils/sbiutils.py
index 400e9ebed..93b42a5cd 100644
--- a/sbi/utils/sbiutils.py
+++ b/sbi/utils/sbiutils.py
@@ -33,24 +33,35 @@ def warn_if_zscoring_changes_data(x: Tensor, duplicate_tolerance: float = 0.1) -
     # Count unique xs.
     num_unique = torch.unique(x, dim=0).numel()
 
-    # z-score.
-    zx = (x - x.mean(0)) / x.std(0)
-
-    # Count again and warn on too many new duplicates.
-    num_unique_z = torch.unique(zx, dim=0).numel()
-
-    if num_unique_z < num_unique * (1 - duplicate_tolerance):
+    # Check we do have different data in the batch
+    if num_unique == 1:
         warnings.warn(
-            """Z-scoring these simulation outputs resulted in {num_unique_z} unique
-            datapoints. Before z-scoring, it had been {num_unique}. This can occur due
-            to numerical inaccuracies when the data covers a large range of values.
-            Consider either setting `z_score_x=False` (but beware that this can be
-            problematic for training the NN) or exclude outliers from your dataset.
-            Note: if you have already set `z_score_x=False`, this warning will still be
-            displayed, but you can ignore it.""",
+            """Variance along batches is 0. Therefore, Z-score could not be computed and will be skipped.
+            Check that data is different along all dimensions.""",
             UserWarning,
         )
 
+        # Skip computation.
+        return
+    else:
+        # z-score.
+        zx = (x - x.mean(0)) / x.std(0)
+
+        # Count again and warn on too many new duplicates.
+        num_unique_z = torch.unique(zx, dim=0).numel()
+
+        if num_unique_z < num_unique * (1 - duplicate_tolerance):
+            warnings.warn(
+                """Z-scoring these simulation outputs resulted in {num_unique_z} unique
+                datapoints. Before z-scoring, it had been {num_unique}. This can occur due
+                to numerical inaccuracies when the data covers a large range of values.
+                Consider either setting `z_score_x=False` (but beware that this can be
+                problematic for training the NN) or exclude outliers from your dataset.
+                Note: if you have already set `z_score_x=False`, this warning will still be
+                displayed, but you can ignore it.""",
+                UserWarning,
+            )
+
 
 def x_shape_from_simulation(batch_x: Tensor) -> torch.Size:
     ndims = batch_x.ndim