diff --git a/sbi/samplers/rejection/rejection.py b/sbi/samplers/rejection/rejection.py
index 5c1d5ffc5..35492ca47 100644
--- a/sbi/samplers/rejection/rejection.py
+++ b/sbi/samplers/rejection/rejection.py
@@ -362,6 +362,4 @@ def accept_reject_sample(
         samples.shape[0] == num_samples
     ), "Number of accepted samples must match required samples."
 
-    # NOTE: Restriction prior does currently require a float as return for the
-    # acceptance rate, which is why we for now also return the minimum acceptance rate.
-    return samples, as_tensor(min_acceptance_rate)
+    return samples, as_tensor(acceptance_rate)
diff --git a/sbi/utils/restriction_estimator.py b/sbi/utils/restriction_estimator.py
index 83bd436f7..e895d0d1a 100644
--- a/sbi/utils/restriction_estimator.py
+++ b/sbi/utils/restriction_estimator.py
@@ -692,6 +692,11 @@ def sample(
                 max_sampling_batch_size=max_sampling_batch_size,
                 alternative_method="sample_with='sir'",
             )
+            # NOTE: This currently requires a float acceptance rate. A previous version
+            # of accept_reject_sample returned a float. In favour to batched sampling
+            # it now returns a tensor.
+            acceptance_rate = acceptance_rate.min().item()
+
             if save_acceptance_rate:
                 self.acceptance_rate = torch.as_tensor(acceptance_rate)
             if print_rejected_frac:
diff --git a/tests/posterior_nn_test.py b/tests/posterior_nn_test.py
index 6b0352f2f..b236e21e0 100644
--- a/tests/posterior_nn_test.py
+++ b/tests/posterior_nn_test.py
@@ -6,7 +6,7 @@
 import pytest
 import torch
 from torch import eye, ones, zeros
-from torch.distributions import MultivariateNormal
+from torch.distributions import Independent, MultivariateNormal, Uniform
 
 from sbi.inference import (
     NLE_A,
@@ -98,13 +98,20 @@ def test_importance_posterior_sample_log_prob(snplre_method: type):
 
 @pytest.mark.parametrize("snpe_method", [NPE_A, NPE_C])
 @pytest.mark.parametrize("x_o_batch_dim", (0, 1, 2))
+@pytest.mark.parametrize("prior", ("mvn", "uniform"))
 def test_batched_sample_log_prob_with_different_x(
-    snpe_method: type, x_o_batch_dim: bool
+    snpe_method: type,
+    x_o_batch_dim: bool,
+    prior: str,
 ):
     num_dim = 2
     num_simulations = 1000
 
-    prior = MultivariateNormal(loc=zeros(num_dim), covariance_matrix=eye(num_dim))
+    # We also want to test on bounded support! Which will invoke leakage correction.
+    if prior == "mvn":
+        prior = MultivariateNormal(loc=zeros(num_dim), covariance_matrix=eye(num_dim))
+    elif prior == "uniform":
+        prior = Independent(Uniform(-1.0 * ones(num_dim), 1.0 * ones(num_dim)), 1)
     simulator = diagonal_linear_gaussian
 
     inference = snpe_method(prior=prior)
@@ -116,6 +123,7 @@ def test_batched_sample_log_prob_with_different_x(
 
     posterior = DirectPosterior(posterior_estimator=posterior_estimator, prior=prior)
 
+    torch.manual_seed(0)
     samples = posterior.sample_batched((10,), x_o)
     batched_log_probs = posterior.log_prob_batched(samples, x_o)
 
@@ -126,6 +134,20 @@ def test_batched_sample_log_prob_with_different_x(
     ), "Sample shape wrong"
     assert batched_log_probs.shape == (10, max(x_o_batch_dim, 1)), "logprob shape wrong"
 
+    # Test consistency with non-batched log_prob
+    # NOTE: Leakage factor is a MC estimate, so we need to relax the tolerance here.
+    if x_o_batch_dim == 0:
+        log_probs = posterior.log_prob(samples, x=x_o)
+        assert torch.allclose(
+            log_probs, batched_log_probs[:, 0], atol=1e-1, rtol=1e-1
+        ), "Batched log probs different from non-batched log probs"
+    else:
+        for idx in range(x_o_batch_dim):
+            log_probs = posterior.log_prob(samples[:, idx], x=x_o[idx])
+            assert torch.allclose(
+                log_probs, batched_log_probs[:, idx], atol=1e-1, rtol=1e-1
+            ), "Batched log probs different from non-batched log probs"
+
 
 @pytest.mark.mcmc
 @pytest.mark.parametrize("snlre_method", [NLE_A, NRE_A, NRE_B, NRE_C, NPE_C])