diff --git a/blackjax/mcmc/integrators.py b/blackjax/mcmc/integrators.py
index 840693f81..be96fa4b1 100644
--- a/blackjax/mcmc/integrators.py
+++ b/blackjax/mcmc/integrators.py
@@ -306,6 +306,7 @@ def esh_dynamics_momentum_update_one_step(
     There are no exponentials e^delta, which prevents overflows when the gradient norm
     is large.
     """
+    del is_last_call
 
     flatten_grads, unravel_fn = ravel_pytree(logdensity_grad)
     flatten_momentum, _ = ravel_pytree(momentum)
@@ -324,11 +325,9 @@ def esh_dynamics_momentum_update_one_step(
         delta
         - jnp.log(2)
         + jnp.log(1 + momentum_proj + (1 - momentum_proj) * zeta**2)
-    )
+    ) * (dims - 1)
     if previous_kinetic_energy_change is not None:
         kinetic_energy_change += previous_kinetic_energy_change
-    if is_last_call:
-        kinetic_energy_change *= dims - 1
     return next_momentum, next_momentum, kinetic_energy_change
 
 
diff --git a/blackjax/mcmc/mclmc.py b/blackjax/mcmc/mclmc.py
index 33f6060c2..26bbda2b8 100644
--- a/blackjax/mcmc/mclmc.py
+++ b/blackjax/mcmc/mclmc.py
@@ -84,7 +84,7 @@ def kernel(
         )
 
         # Langevin-like noise
-        momentum, dim = partially_refresh_momentum(
+        momentum = partially_refresh_momentum(
             momentum=momentum, rng_key=rng_key, L=L, step_size=step_size
         )
 
@@ -93,8 +93,7 @@ def kernel(
         ), MCLMCInfo(
             logdensity=logdensity,
             energy_change=kinetic_change - logdensity + state.logdensity,
-            # TODO: Potential bug here, see #625
-            kinetic_change=kinetic_change * (dim - 1),
+            kinetic_change=kinetic_change,
         )
 
     return kernel
@@ -191,4 +190,4 @@ def partially_refresh_momentum(momentum, rng_key, step_size, L):
     dim = m.shape[0]
     nu = jnp.sqrt((jnp.exp(2 * step_size / L) - 1.0) / dim)
     z = nu * normal(rng_key, shape=m.shape, dtype=m.dtype)
-    return unravel_fn((m + z) / jnp.linalg.norm(m + z)), dim
+    return unravel_fn((m + z) / jnp.linalg.norm(m + z))
diff --git a/tests/mcmc/test_integrators.py b/tests/mcmc/test_integrators.py
index 2f5020d00..2ef285dd2 100644
--- a/tests/mcmc/test_integrators.py
+++ b/tests/mcmc/test_integrators.py
@@ -228,6 +228,59 @@ def test_esh_momentum_update(self, dims):
         next_momentum1, *_ = update_stable(momentum, gradient, step_size, 1.0)
         np.testing.assert_array_almost_equal(next_momentum, next_momentum1)
 
+    @chex.all_variants(with_pmap=False)
+    def test_noneuclidean_leapfrog(self):
+        cov = jnp.asarray([[1.0, 0.5, 0.1], [0.5, 2.0, -0.1], [0.1, -0.1, 3.0]])
+        logdensity_fn = lambda x: stats.multivariate_normal.logpdf(
+            x, jnp.zeros([3]), cov
+        )
+
+        step = self.variant(integrators.noneuclidean_leapfrog(logdensity_fn))
+
+        rng = jax.random.key(4263456)
+        key0, key1 = jax.random.split(rng, 2)
+        position_init = jax.random.normal(key0, (3,))
+        momentum_init = generate_unit_vector(key1, position_init)
+        step_size = 0.0001
+        initial_state = integrators.new_integrator_state(
+            logdensity_fn, position_init, momentum_init
+        )
+        next_state, kinetic_energy_change = step(initial_state, step_size)
+
+        # explicit integration
+        op1 = esh_dynamics_momentum_update_one_step
+        op2 = integrators.euclidean_position_update_fn(logdensity_fn)
+        position, momentum, _, logdensity_grad = initial_state
+        momentum, kinetic_grad, kinetic_energy_change0 = op1(
+            momentum,
+            logdensity_grad,
+            step_size,
+            0.5,
+            None,
+        )
+        position, logdensity, logdensity_grad, position_update_info = op2(
+            position,
+            kinetic_grad,
+            step_size,
+            1.0,
+            None,
+        )
+        momentum, kinetic_grad, kinetic_energy_change1 = op1(
+            momentum,
+            logdensity_grad,
+            step_size,
+            0.5,
+            None,
+        )
+        next_state_ = integrators.IntegratorState(
+            position, momentum, logdensity, logdensity_grad
+        )
+
+        chex.assert_trees_all_close(next_state, next_state_)
+        np.testing.assert_almost_equal(
+            kinetic_energy_change, kinetic_energy_change0 + kinetic_energy_change1
+        )
+
     @chex.all_variants(with_pmap=False)
     @parameterized.parameters(
         [