diff --git a/blackjax/util.py b/blackjax/util.py
index f667d147a..43f9977ec 100644
--- a/blackjax/util.py
+++ b/blackjax/util.py
@@ -9,6 +9,7 @@
 from jax.tree_util import tree_leaves
 
 from blackjax.base import Info, State
+from blackjax.progress_bar import progress_bar_scan
 from blackjax.types import Array, ArrayLikeTree, ArrayTree, PRNGKey
 
 
@@ -144,6 +145,7 @@ def run_inference_algorithm(
     initial_state_or_position,
     inference_algorithm,
     num_steps,
+    progress_bar: bool = False,
 ) -> tuple[State, State, Info]:
     """Wrapper to run an inference algorithm.
 
@@ -171,14 +173,20 @@ def run_inference_algorithm(
     except TypeError:
         # We assume initial_state is already in the right format.
         initial_state = initial_state_or_position
-    initial_state = initial_state_or_position
 
     keys = split(rng_key, num_steps)
 
     @jit
-    def one_step(state, rng_key):
+    def _one_step(state, xs):
+        _, rng_key = xs
         state, info = inference_algorithm.step(rng_key, state)
         return state, (state, info)
 
-    final_state, (state_history, info_history) = lax.scan(one_step, initial_state, keys)
+    if progress_bar:
+        one_step = progress_bar_scan(num_steps)(_one_step)
+    else:
+        one_step = _one_step
+
+    xs = (jnp.arange(num_steps), keys)
+    final_state, (state_history, info_history) = lax.scan(one_step, initial_state, xs)
     return final_state, state_history, info_history
diff --git a/tests/test_util.py b/tests/test_util.py
new file mode 100644
index 000000000..5bc35e50a
--- /dev/null
+++ b/tests/test_util.py
@@ -0,0 +1,50 @@
+import chex
+import jax
+import jax.numpy as jnp
+from absl.testing import absltest, parameterized
+
+from blackjax.mcmc.hmc import hmc
+from blackjax.util import run_inference_algorithm
+
+
+class RunInferenceAlgorithmTest(chex.TestCase):
+    def setUp(self):
+        super().setUp()
+        self.key = jax.random.key(42)
+        self.algorithm = hmc(
+            logdensity_fn=self.logdensity_fn,
+            inverse_mass_matrix=jnp.eye(2),
+            step_size=1.0,
+            num_integration_steps=1000,
+        )
+        self.num_steps = 10
+
+    def check_compatible(self, initial_state_or_position, progress_bar):
+        """
+        Runs 10 steps with `run_inference_algorithm` starting with
+        `initial_state_or_position` and potentially a progress bar.
+        """
+        _ = run_inference_algorithm(
+            self.key,
+            initial_state_or_position,
+            self.algorithm,
+            self.num_steps,
+            progress_bar,
+        )
+
+    @parameterized.parameters([True, False])
+    def test_compatible_with_initial_pos(self, progress_bar):
+        self.check_compatible(jnp.array([1.0, 1.0]), progress_bar)
+
+    @parameterized.parameters([True, False])
+    def test_compatible_with_initial_state(self, progress_bar):
+        state = self.algorithm.init(jnp.array([1.0, 1.0]))
+        self.check_compatible(state, progress_bar)
+
+    @staticmethod
+    def logdensity_fn(x):
+        return -0.5 * jnp.sum(jnp.square(x))
+
+
+if __name__ == "__main__":
+    absltest.main()