diff --git a/sbi/inference/posteriors/direct_posterior.py b/sbi/inference/posteriors/direct_posterior.py
index 76b9fdf48..e6b684fab 100644
--- a/sbi/inference/posteriors/direct_posterior.py
+++ b/sbi/inference/posteriors/direct_posterior.py
@@ -104,12 +104,19 @@ def sample(
                 `sbi` v0.17.2 or older. If it is set, we instantly raise an error.
             show_progress_bars: Whether to show sampling progress monitor.
         """
-
         num_samples = torch.Size(sample_shape).numel()
         x = self._x_else_default_x(x)
         x = reshape_to_batch_event(
             x, event_shape=self.posterior_estimator.condition_shape
         )
+        if x.shape[0] > 1:
+            raise ValueError(
+                ".sample() supports only `batchsize == 1`. If you intend "
+                "to sample multiple observations, use `.sample_batched()`. "
+                "If you intend to sample i.i.d. observations, set up the "
+                "posterior density estimator with an appropriate permutation "
+                "invariant embedding net."
+            )
 
         max_sampling_batch_size = (
             self.max_sampling_batch_size
@@ -132,7 +139,7 @@ def sample(
             max_sampling_batch_size=max_sampling_batch_size,
             proposal_sampling_kwargs={"condition": x},
             alternative_method="build_posterior(..., sample_with='mcmc')",
-        )[0]
+        )[0]  # [0] to return only samples, not acceptance probabilities.
 
         return samples[:, 0]  # Remove batch dimension.
 
@@ -221,9 +228,14 @@ def log_prob(
         x_density_estimator = reshape_to_batch_event(
             x, event_shape=self.posterior_estimator.condition_shape
         )
-        assert (
-            x_density_estimator.shape[0] == 1
-        ), ".log_prob() supports only `batchsize == 1`."
+        if x_density_estimator.shape[0] > 1:
+            raise ValueError(
+                ".log_prob() supports only `batchsize == 1`. If you intend "
+                "to evaluate given multiple observations, use `.log_prob_batched()`. "
+                "If you intend to evaluate given i.i.d. observations, set up the "
+                "posterior density estimator with an appropriate permutation "
+                "invariant embedding net."
+            )
 
         self.posterior_estimator.eval()