diff --git a/sbi/inference/potentials/likelihood_based_potential.py b/sbi/inference/potentials/likelihood_based_potential.py
index f382968cd..20a831899 100644
--- a/sbi/inference/potentials/likelihood_based_potential.py
+++ b/sbi/inference/potentials/likelihood_based_potential.py
@@ -1,7 +1,8 @@
 # This file is part of sbi, a toolkit for simulation-based inference. sbi is licensed
 # under the Apache License Version 2.0, see <https://www.apache.org/licenses/>
 
-from typing import Callable, Optional, Tuple
+import warnings
+from typing import Callable, List, Optional, Tuple
 
 import torch
 from torch import Tensor
@@ -115,6 +116,38 @@ def __call__(self, theta: Tensor, track_gradients: bool = True) -> Tensor:
                 )
             return log_likelihood_batches + self.prior.log_prob(theta)  # type: ignore
 
+    def condition_on(self, condition: Tensor, dims_to_sample: List[int]) -> Callable:
+        """Returns a potential conditioned on a subset of theta dimensions.
+
+        The condition is a part of theta, but is assumed to correspond to a batch of iid
+        x_o.
+
+        Args:
+            condition: The condition to fix.
+            dims_to_sample: The indices of the parameters to sample.
+
+        Returns:
+            A potential function conditioned on the condition.
+        """
+
+        def conditioned_potential(
+            theta: Tensor, x_o: Optional[Tensor] = None, track_gradients: bool = True
+        ) -> Tensor:
+            assert (
+                len(dims_to_sample) == theta.shape[1] - condition.shape[1]
+            ), "dims_to_sample must match the number of parameters to sample."
+            theta_without_condition = theta[:, dims_to_sample]
+
+            return _log_likelihood_with_iid_condition(
+                x=x_o or self.x_o,
+                theta_without_condition=theta_without_condition,
+                condition=condition,
+                estimator=self.likelihood_estimator,
+                track_gradients=track_gradients,
+            )
+
+        return conditioned_potential
+
 
 def _log_likelihoods_over_trials(
     x: Tensor,
@@ -172,6 +205,67 @@ def _log_likelihoods_over_trials(
     return log_likelihood_trial_sum
 
 
+def _log_likelihood_with_iid_condition(
+    x: Tensor,
+    theta_without_condition: Tensor,
+    condition: Tensor,
+    estimator: ConditionalDensityEstimator,
+    track_gradients: bool = False,
+) -> Tensor:
+    """Return log likelihoods summed over iid trials of `x` with a matching batch of
+    conditions.
+
+    This function is different from `_log_likelihoods_over_trials` in that it moves the
+    iid batch dimension of `x` onto the batch dimension of `theta`. This is useful when
+    the likelihood estimator is conditioned on a batch of conditions that are iid with
+    the batch of `x`. It avoid the evaluation of the likelihood for every combination of
+    `x` and `condition`. Instead, it manually constructs a batch covering all
+    combination of iid trial and theta batch and reshapes to sum over the iid
+    likelihoods.
+
+    Args:
+        x: Batch of iid data of shape `(iid_dim, *event_shape)`.
+        theta_without_condition: Batch of parameters `(batch_dim, *event_shape)`
+        condition: Batch of conditions of shape `(iid_dim, *condition_shape)`.
+        estimator: DensityEstimator.
+        track_gradients: Whether to track gradients.
+
+    Returns:
+        log_likelihood_trial_sum: log likelihood for each parameter, summed over all
+            batch entries (iid trials) in `x`.
+    """
+    assert (
+        condition.shape[0] == x.shape[0]
+    ), "Condition and iid x must have the same batch size."
+    num_trials = x.shape[0]
+    num_theta = theta_without_condition.shape[0]
+    x = reshape_to_sample_batch_event(
+        x, event_shape=x.shape[1:], leading_is_sample=True
+    )
+
+    # move the iid batch dimension onto the batch dimension of theta and repeat it there
+    x_expanded = x.reshape(1, num_trials, -1).repeat_interleave(num_theta, dim=1)
+    # for this to work we construct theta and condition to cover all combinations in the
+    # trial batch and the theta batch.
+    theta = torch.cat(
+        [
+            theta_without_condition.repeat(num_trials, 1),  # repeat ABAB
+            condition.repeat_interleave(num_theta, dim=0),  # repeat AABB
+        ],
+        dim=-1,
+    )
+
+    with torch.set_grad_enabled(track_gradients):
+        # Calculate likelihood in one batch. Returns (1, num_trials * theta_batch_size)
+        log_likelihood_trial_batch = estimator.log_prob(x_expanded, condition=theta)
+        # Reshape to (x-trials x parameters), sum over trial-log likelihoods.
+        log_likelihood_trial_sum = log_likelihood_trial_batch.reshape(
+            num_trials, num_theta
+        ).sum(0)
+
+    return log_likelihood_trial_sum
+
+
 def mixed_likelihood_estimator_based_potential(
     likelihood_estimator: MixedDensityEstimator,
     prior: Distribution,
@@ -192,6 +286,13 @@ def mixed_likelihood_estimator_based_potential(
         to unconstrained space.
     """
 
+    warnings.warn(
+        "This function is deprecated and will be removed in a future release. Use "
+        "`likelihood_estimator_based_potential` instead.",
+        DeprecationWarning,
+        stacklevel=2,
+    )
+
     device = str(next(likelihood_estimator.discrete_net.parameters()).device)
 
     potential_fn = MixedLikelihoodBasedPotential(
@@ -212,6 +313,13 @@ def __init__(
     ):
         super().__init__(likelihood_estimator, prior, x_o, device)
 
+        warnings.warn(
+            "This function is deprecated and will be removed in a future release. Use "
+            "`LikelihoodBasedPotential` instead.",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+
     def __call__(self, theta: Tensor, track_gradients: bool = True) -> Tensor:
         prior_log_prob = self.prior.log_prob(theta)  # type: ignore
 
@@ -231,7 +339,6 @@ def __call__(self, theta: Tensor, track_gradients: bool = True) -> Tensor:
         with torch.set_grad_enabled(track_gradients):
             # Call the specific log prob method of the mixed likelihood estimator as
             # this optimizes the evaluation of the discrete data part.
-            # TODO log_prob_iid
             log_likelihood_trial_batch = self.likelihood_estimator.log_prob(
                 input=x,
                 condition=theta.to(self.device),
diff --git a/sbi/inference/trainers/nle/mnle.py b/sbi/inference/trainers/nle/mnle.py
index d01ce1e91..83622eaea 100644
--- a/sbi/inference/trainers/nle/mnle.py
+++ b/sbi/inference/trainers/nle/mnle.py
@@ -7,7 +7,7 @@
 from torch.distributions import Distribution
 
 from sbi.inference.posteriors import MCMCPosterior, RejectionPosterior, VIPosterior
-from sbi.inference.potentials import mixed_likelihood_estimator_based_potential
+from sbi.inference.potentials import likelihood_estimator_based_potential
 from sbi.inference.trainers.nle.nle_base import LikelihoodEstimator
 from sbi.neural_nets.estimators import MixedDensityEstimator
 from sbi.sbi_types import TensorboardSummaryWriter, TorchModule
@@ -155,9 +155,7 @@ def build_posterior(
         (
             potential_fn,
             theta_transform,
-        ) = mixed_likelihood_estimator_based_potential(
-            likelihood_estimator=likelihood_estimator, prior=prior, x_o=None
-        )
+        ) = likelihood_estimator_based_potential(likelihood_estimator, prior, x_o=None)
 
         if sample_with == "mcmc":
             self._posterior = MCMCPosterior(
diff --git a/sbi/utils/conditional_density_utils.py b/sbi/utils/conditional_density_utils.py
index d6c73b7c9..829f5e1df 100644
--- a/sbi/utils/conditional_density_utils.py
+++ b/sbi/utils/conditional_density_utils.py
@@ -293,7 +293,7 @@ def __init__(
             masked outside of prior.
         """
         condition = torch.atleast_2d(condition)
-        if condition.shape[0] != 1:
+        if condition.shape[0] > 1:
             raise ValueError("Condition with batch size > 1 not supported.")
 
         self.potential_fn = potential_fn
diff --git a/sbi/utils/sbiutils.py b/sbi/utils/sbiutils.py
index fcb5953d9..fc01d4dbd 100644
--- a/sbi/utils/sbiutils.py
+++ b/sbi/utils/sbiutils.py
@@ -60,8 +60,8 @@ def warn_if_zscoring_changes_data(x: Tensor, duplicate_tolerance: float = 0.1) -
 
         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 "
+                f"Z-scoring these simulation outputs resulted in {num_unique_z} unique "
+                f"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 "
diff --git a/tests/mnle_test.py b/tests/mnle_test.py
index a95a2a6ac..b242f477f 100644
--- a/tests/mnle_test.py
+++ b/tests/mnle_test.py
@@ -1,29 +1,31 @@
 # This file is part of sbi, a toolkit for simulation-based inference. sbi is licensed
 # under the Apache License Version 2.0, see <https://www.apache.org/licenses/>
 
+from typing import Union
+
 import pytest
 import torch
 from pyro.distributions import InverseGamma
-from torch.distributions import Beta, Binomial, Categorical, Gamma
+from torch import Tensor
+from torch.distributions import Beta, Binomial, Distribution, Gamma
 
 from sbi.inference import MNLE, MCMCPosterior
 from sbi.inference.posteriors.rejection_posterior import RejectionPosterior
 from sbi.inference.posteriors.vi_posterior import VIPosterior
 from sbi.inference.potentials.base_potential import BasePotential
 from sbi.inference.potentials.likelihood_based_potential import (
-    MixedLikelihoodBasedPotential,
+    likelihood_estimator_based_potential,
 )
 from sbi.neural_nets import likelihood_nn
 from sbi.neural_nets.embedding_nets import FCEmbedding
 from sbi.utils import BoxUniform, mcmc_transform
-from sbi.utils.conditional_density_utils import ConditionedPotential
 from sbi.utils.torchutils import atleast_2d, process_device
 from sbi.utils.user_input_checks_utils import MultipleIndependent
 from tests.test_utils import check_c2st
 
 
 # toy simulator for mixed data
-def mixed_simulator(theta, stimulus_condition=2.0):
+def mixed_simulator(theta: Tensor, stimulus_condition: Union[Tensor, float] = 2.0):
     """Simulator for mixed data."""
     # Extract parameters
     beta, ps = theta[:, :1], theta[:, 1:]
@@ -190,11 +192,28 @@ def test_mnle_accuracy_with_different_samplers_and_trials(
 
 
 class BinomialGammaPotential(BasePotential):
-    def __init__(self, prior, x_o, concentration_scaling=1.0, device="cpu"):
+    """Binomial-Gamma potential for mixed data."""
+
+    def __init__(
+        self,
+        prior: Distribution,
+        x_o: Tensor,
+        concentration_scaling: Union[Tensor, float] = 1.0,
+        device="cpu",
+    ):
         super().__init__(prior, x_o, device)
+
+        # concentration_scaling needs to be a float or match the batch size
+        if isinstance(concentration_scaling, Tensor):
+            num_trials = x_o.shape[0]
+            assert concentration_scaling.shape[0] == num_trials
+
+            # Reshape to match convention (batch_size, num_trials, *event_shape)
+            concentration_scaling = concentration_scaling.reshape(1, num_trials, -1)
+
         self.concentration_scaling = concentration_scaling
 
-    def __call__(self, theta, track_gradients: bool = True):
+    def __call__(self, theta: Tensor, track_gradients: bool = True) -> Tensor:
         theta = atleast_2d(theta)
 
         with torch.set_grad_enabled(track_gradients):
@@ -202,11 +221,12 @@ def __call__(self, theta, track_gradients: bool = True):
 
         return iid_ll + self.prior.log_prob(theta)
 
-    def iid_likelihood(self, theta):
+    def iid_likelihood(self, theta: Tensor) -> Tensor:
         batch_size = theta.shape[0]
         num_trials = self.x_o.shape[0]
         theta = theta.reshape(batch_size, 1, -1)
         beta, rho = theta[:, :, :1], theta[:, :, 1:]
+
         # vectorized
         logprob_choices = Binomial(probs=rho).log_prob(
             self.x_o[:, 1:].reshape(1, num_trials, -1)
@@ -233,18 +253,22 @@ def test_mnle_with_experimental_conditions(mcmc_params_accurate: dict):
     categorical parameter is set to a fixed value (conditioned posterior), and the
     accuracy of the conditioned posterior is tested against the true posterior.
     """
-    num_simulations = 6000
-    num_samples = 500
+    num_simulations = 10000
+    num_samples = 1000
 
-    def sim_wrapper(theta):
+    def sim_wrapper(
+        theta_and_condition: Tensor, last_idx_parameters: int = 2
+    ) -> Tensor:
         # simulate with experiment conditions
-        return mixed_simulator(theta[:, :2], theta[:, 2:] + 1)
+        theta = theta_and_condition[:, :last_idx_parameters]
+        condition = theta_and_condition[:, last_idx_parameters:]
+        return mixed_simulator(theta, condition)
 
     proposal = MultipleIndependent(
         [
             Gamma(torch.tensor([1.0]), torch.tensor([0.5])),
             Beta(torch.tensor([2.0]), torch.tensor([2.0])),
-            Categorical(probs=torch.ones(1, 3)),
+            BoxUniform(torch.tensor([0.0]), torch.tensor([1.0])),
         ],
         validate_args=False,
     )
@@ -254,22 +278,27 @@ def sim_wrapper(theta):
     assert x.shape == (num_simulations, 2)
 
     num_trials = 10
-    theta_o = proposal.sample((1,))
-    theta_o[0, 2] = 2.0  # set condition to 2 as in original simulator.
-    x_o = sim_wrapper(theta_o.repeat(num_trials, 1))
+    theta_and_condition = proposal.sample((num_trials,))
+    # use only a single parameter (iid trials)
+    theta_o = theta_and_condition[:1, :2].repeat(num_trials, 1)
+    # but different conditions
+    condition_o = theta_and_condition[:, 2:]
+    theta_and_conditions_o = torch.cat((theta_o, condition_o), dim=1)
+
+    x_o = sim_wrapper(theta_and_conditions_o)
 
     mcmc_kwargs = dict(
         method="slice_np_vectorized", init_strategy="proposal", **mcmc_params_accurate
     )
 
     # MNLE
-    trainer = MNLE(proposal)
-    estimator = trainer.append_simulations(theta, x).train(training_batch_size=1000)
-
-    potential_fn = MixedLikelihoodBasedPotential(estimator, proposal, x_o)
+    estimator_fun = likelihood_nn(model="mnle", z_score_x=None)
+    trainer = MNLE(proposal, estimator_fun)
+    estimator = trainer.append_simulations(theta, x).train()
 
-    conditioned_potential_fn = ConditionedPotential(
-        potential_fn, condition=theta_o, dims_to_sample=[0, 1]
+    potential_fn, _ = likelihood_estimator_based_potential(estimator, proposal, x_o)
+    conditioned_potential_fn = potential_fn.condition_on(
+        condition_o, dims_to_sample=[0, 1]
     )
 
     # True posterior samples
@@ -283,10 +312,7 @@ def sim_wrapper(theta):
     prior_transform = mcmc_transform(prior)
     true_posterior_samples = MCMCPosterior(
         BinomialGammaPotential(
-            prior,
-            atleast_2d(x_o),
-            concentration_scaling=float(theta_o[0, 2])
-            + 1.0,  # add one because the sim_wrapper adds one (see above)
+            prior, atleast_2d(x_o), concentration_scaling=condition_o
         ),
         theta_transform=prior_transform,
         proposal=prior,
@@ -303,5 +329,5 @@ def sim_wrapper(theta):
     check_c2st(
         cond_samples,
         true_posterior_samples,
-        alg=f"MNLE trained with {num_simulations}",
+        alg=f"MNLE trained with {num_simulations} simulations",
     )