diff --git a/metastable_baselines/distributions/distributions.py b/metastable_baselines/distributions/distributions.py
index bff2443..879a8ba 100644
--- a/metastable_baselines/distributions/distributions.py
+++ b/metastable_baselines/distributions/distributions.py
@@ -206,6 +206,21 @@ class UniversalGaussianDistribution(SB3_Distribution):
 
         return mean_actions, chol
 
+    def proba_distribution_from_sqrt(self, mean_actions: th.Tensor, cov_sqrt: th.Tensor, latent_pi: nn.Module) -> "UniversalGaussianDistribution":
+        """
+        Create the distribution given its parameters (mean, cov_sqrt)
+
+        :param mean_actions:
+        :param cov_sqrt:
+        :return:
+        """
+        cov = cov_sqrt.T @ cov_sqrt
+        chol = th.linalg.cholesky(cov)
+
+        self.cov_sqrt = cov_sqrt
+
+        return self.proba_distribution(mean_actions, chol, latent_pi)
+
     def proba_distribution(self, mean_actions: th.Tensor, chol: th.Tensor, latent_pi: nn.Module) -> "UniversalGaussianDistribution":
         """
         Create the distribution given its parameters (mean, chol)
diff --git a/metastable_baselines/ppo/policies.py b/metastable_baselines/ppo/policies.py
index 63a99c9..f476b94 100644
--- a/metastable_baselines/ppo/policies.py
+++ b/metastable_baselines/ppo/policies.py
@@ -35,6 +35,8 @@ from stable_baselines3.common.torch_layers import (
     NatureCNN,
 )
 
+from metastable_baselines.projections.w2_projection_layer import WassersteinProjectionLayer
+
 from ..distributions import UniversalGaussianDistribution, make_proba_distribution
 
 
@@ -286,6 +288,17 @@ class ActorCriticPolicy(BasePolicy):
         """
         mean_actions = self.action_net(latent_pi)
 
+        if isinstance(self.projection, WassersteinProjectionLayer):
+            if isinstance(self.action_dist, UniversalGaussianDistribution):
+                cov_sqrt = self.chol_net(latent_pi)
+                dist = self.action_dist.proba_distribution_from_sqrt(
+                    mean_actions, cov_sqrt, latent_pi)
+                self.chol = dist.chol
+                return dist
+            else:
+                raise Exception(
+                    'Need to use UniversalGaussianDistribution to use WassersteinProjection (uses sqrt-induced-cov)')
+
         if isinstance(self.action_dist, DiagGaussianDistribution):
             return self.action_dist.proba_distribution(mean_actions, self.log_std)
         elif isinstance(self.action_dist, CategoricalDistribution):