diff --git a/sbi/inference/posteriors/vi_posterior.py b/sbi/inference/posteriors/vi_posterior.py
index 4bd29a4a3..95529b7dd 100644
--- a/sbi/inference/posteriors/vi_posterior.py
+++ b/sbi/inference/posteriors/vi_posterior.py
@@ -115,7 +115,7 @@ def __init__(
             self._prior = q._prior
         else:
             raise ValueError(
-                "We could not find a suitable prior distribution within `potential_fn`"
+                "We could not find a suitable prior distribution within `potential_fn` "
                 "or `q` (if a VIPosterior is given). Please explicitly specify a prior."
             )
         move_all_tensor_to_device(self._prior, device)
@@ -461,9 +461,12 @@ def train(
                 self.evaluate(quality_control_metric=quality_control_metric)
             except Exception as e:
                 print(
-                    f"Quality control did not work, we reset the variational \
-                        posterior,please check your setting. \
-                        \n Following error occured {e}"
+                    f"Quality control showed a low quality of the variational "
+                    f"posterior. We are automatically retraining the variational "
+                    f"posterior from scratch with a smaller learning rate. "
+                    f"Alternatively, if you want to skip quality control, please "
+                    f"retrain with `VIPosterior.train(..., quality_control=False)`. "
+                    f"\nThe error that occured is: {e}"
                 )
                 self.train(
                     learning_rate=learning_rate * 0.1,
diff --git a/tests/potential_test.py b/tests/potential_test.py
new file mode 100644
index 000000000..4784e4534
--- /dev/null
+++ b/tests/potential_test.py
@@ -0,0 +1,60 @@
+# This file is part of sbi, a toolkit for simulation-based inference. sbi is licensed
+# under the Affero General Public License v3, see <https://www.gnu.org/licenses/>.
+
+from __future__ import annotations
+
+import pytest
+import torch
+from torch import eye, ones, zeros
+from torch.distributions import MultivariateNormal
+
+from sbi.inference import (
+    ImportanceSamplingPosterior,
+    MCMCPosterior,
+    RejectionPosterior,
+    VIPosterior,
+)
+
+
+@pytest.mark.parametrize(
+    "sampling_method",
+    [ImportanceSamplingPosterior, MCMCPosterior, RejectionPosterior, VIPosterior],
+)
+def test_callable_potential(sampling_method):
+    dim = 2
+    mean = 2.5
+    cov = 2.0
+    x_o = 1 * ones((dim,))
+    target_density = MultivariateNormal(mean * ones((dim,)), cov * eye(dim))
+
+    def potential(theta, x_o, **kwargs):
+        return target_density.log_prob(theta + x_o)
+
+    proposal = MultivariateNormal(zeros((dim,)), 5 * eye(dim))
+
+    if sampling_method == ImportanceSamplingPosterior:
+        approx_density = sampling_method(
+            potential_fn=potential, proposal=proposal, method="sir"
+        )
+        approx_samples = approx_density.sample((1024,), oversampling_factor=1024, x=x_o)
+    elif sampling_method == MCMCPosterior:
+        approx_density = sampling_method(potential_fn=potential, proposal=proposal)
+        approx_samples = approx_density.sample(
+            (1024,), x=x_o, num_chains=100, method="slice_np_vectorized"
+        )
+    elif sampling_method == VIPosterior:
+        approx_density = sampling_method(
+            potential_fn=potential, prior=proposal
+        ).set_default_x(x_o)
+        approx_density = approx_density.train()
+        approx_samples = approx_density.sample((1024,))
+    elif sampling_method == RejectionPosterior:
+        approx_density = sampling_method(
+            potential_fn=potential, proposal=proposal
+        ).set_default_x(x_o)
+        approx_samples = approx_density.sample((1024,))
+
+    sample_mean = torch.mean(approx_samples, dim=0)
+    sample_std = torch.std(approx_samples, dim=0)
+    assert torch.allclose(sample_mean, torch.as_tensor(mean) - x_o, atol=0.2)
+    assert torch.allclose(sample_std, torch.sqrt(torch.as_tensor(cov)), atol=0.1)