diff --git a/blackjax/adaptation/mclmc_adaptation.py b/blackjax/adaptation/mclmc_adaptation.py
index 3365526b3..831586201 100644
--- a/blackjax/adaptation/mclmc_adaptation.py
+++ b/blackjax/adaptation/mclmc_adaptation.py
@@ -20,7 +20,7 @@
 from jax.flatten_util import ravel_pytree
 
 from blackjax.diagnostics import effective_sample_size
-from blackjax.util import incremental_value_update, pytree_size
+from blackjax.util import generate_unit_vector, incremental_value_update, pytree_size
 
 
 class MCLMCAdaptationState(NamedTuple):
@@ -147,6 +147,8 @@ def predictor(previous_state, params, adaptive_state, rng_key):
 
         time, x_average, step_size_max = adaptive_state
 
+        rng_key, nan_key = jax.random.split(rng_key)
+
         # dynamics
         next_state, info = kernel(params.sqrt_diag_cov)(
             rng_key=rng_key,
@@ -162,6 +164,7 @@ def predictor(previous_state, params, adaptive_state, rng_key):
             params.step_size,
             step_size_max,
             info.energy_change,
+            nan_key,
         )
 
         # Warning: var = 0 if there were nans, but we will give it a very small weight
@@ -203,7 +206,7 @@ def step(iteration_state, weight_and_key):
         streaming_avg = incremental_value_update(
             expectation=jnp.array([x, jnp.square(x)]),
             incremental_val=streaming_avg,
-            weight=(1 - mask) * success * params.step_size,
+            weight=mask * success * params.step_size,
         )
 
         return (state, params, adaptive_state, streaming_avg), None
@@ -233,7 +236,7 @@ def L_step_size_adaptation(state, params, num_steps, rng_key):
         )
 
         # we use the last num_steps2 to compute the diagonal preconditioner
-        mask = 1 - jnp.concatenate((jnp.zeros(num_steps1), jnp.ones(num_steps2)))
+        mask = jnp.concatenate((jnp.zeros(num_steps1), jnp.ones(num_steps2)))
 
         # run the steps
         state, params, _, (_, average) = run_steps(
@@ -298,7 +301,9 @@ def step(state, key):
     return adaptation_L
 
 
-def handle_nans(previous_state, next_state, step_size, step_size_max, kinetic_change):
+def handle_nans(
+    previous_state, next_state, step_size, step_size_max, kinetic_change, key
+):
     """if there are nans, let's reduce the stepsize, and not update the state. The
     function returns the old state in this case."""
 
@@ -311,4 +316,13 @@ def handle_nans(previous_state, next_state, step_size, step_size_max, kinetic_ch
         (next_state, step_size_max, kinetic_change),
         (previous_state, step_size * reduced_step_size, 0.0),
     )
+
+    state = jax.lax.cond(
+        jnp.isnan(next_state.logdensity),
+        lambda: state._replace(
+            momentum=generate_unit_vector(key, previous_state.position)
+        ),
+        lambda: state,
+    )
+
     return nonans, state, step_size, kinetic_change