diff --git a/fancy_rl/projections/base_projection.py b/fancy_rl/projections/base_projection.py
index 31f1fa0..3ceb5d1 100644
--- a/fancy_rl/projections/base_projection.py
+++ b/fancy_rl/projections/base_projection.py
@@ -1,16 +1,71 @@
 from abc import ABC, abstractmethod
 import torch
-from typing import Dict
+from torch import nn
+from typing import Dict, List
 
-class BaseProjection(ABC, torch.nn.Module):
-    def __init__(self, in_keys: list[str], out_keys: list[str]):
+class BaseProjection(nn.Module, ABC):
+    def __init__(self, in_keys: List[str], out_keys: List[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01, contextual_std: bool = True):
         super().__init__()
+        self._validate_in_keys(in_keys)
+        self._validate_out_keys(out_keys)
         self.in_keys = in_keys
         self.out_keys = out_keys
+        self.trust_region_coeff = trust_region_coeff
+        self.mean_bound = mean_bound
+        self.cov_bound = cov_bound
+        self.full_cov = "scale_tril" in in_keys
+        self.contextual_std = contextual_std
+
+    def _validate_in_keys(self, keys: List[str]):
+        valid_keys = {"loc", "scale", "scale_tril", "old_loc", "old_scale", "old_scale_tril"}
+        if not set(keys).issubset(valid_keys):
+            raise ValueError(f"Invalid in_keys: {keys}. Must be a subset of {valid_keys}")
+        if "loc" not in keys or "old_loc" not in keys:
+            raise ValueError("Both 'loc' and 'old_loc' must be included in in_keys")
+        if ("scale" in keys) != ("old_scale" in keys) or ("scale_tril" in keys) != ("old_scale_tril" in keys):
+            raise ValueError("in_keys must have matching 'scale'/'old_scale' or 'scale_tril'/'old_scale_tril'")
+
+    def _validate_out_keys(self, keys: List[str]):
+        valid_keys = {"loc", "scale", "scale_tril"}
+        if not set(keys).issubset(valid_keys):
+            raise ValueError(f"Invalid out_keys: {keys}. Must be a subset of {valid_keys}")
+        if "loc" not in keys:
+            raise ValueError("'loc' must be included in out_keys")
+        if "scale" not in keys and "scale_tril" not in keys:
+            raise ValueError("Either 'scale' or 'scale_tril' must be included in out_keys")
 
     @abstractmethod
     def project(self, policy_params: Dict[str, torch.Tensor], old_policy_params: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
         pass
 
-    def forward(self, policy_params: Dict[str, torch.Tensor], old_policy_params: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
-        return self.project(policy_params, old_policy_params)
\ No newline at end of file
+    @abstractmethod
+    def get_trust_region_loss(self, policy_params: Dict[str, torch.Tensor], proj_policy_params: Dict[str, torch.Tensor]) -> torch.Tensor:
+        pass
+
+    def forward(self, tensordict):
+        policy_params = {}
+        old_policy_params = {}
+        
+        for key in self.in_keys:
+            if key not in tensordict:
+                raise KeyError(f"Key '{key}' not found in tensordict. Available keys: {tensordict.keys()}")
+            
+            if key.startswith("old_"):
+                old_policy_params[key[4:]] = tensordict[key]
+            else:
+                policy_params[key] = tensordict[key]
+
+        projected_params = self.project(policy_params, old_policy_params)
+        return projected_params
+
+    def _calc_covariance(self, params: Dict[str, torch.Tensor]) -> torch.Tensor:
+        if not self.full_cov:
+            return torch.diag_embed(params["scale"].pow(2))
+        else:
+            return torch.matmul(params["scale_tril"], params["scale_tril"].transpose(-1, -2))
+
+    def _calc_scale_or_scale_tril(self, cov: torch.Tensor) -> torch.Tensor:
+        if not self.full_cov:
+            return torch.sqrt(cov.diagonal(dim1=-2, dim2=-1))
+        else:
+            return torch.linalg.cholesky(cov)
\ No newline at end of file
diff --git a/fancy_rl/projections/frobenius_projection.py b/fancy_rl/projections/frobenius_projection.py
index 9ad3480..2a92c04 100644
--- a/fancy_rl/projections/frobenius_projection.py
+++ b/fancy_rl/projections/frobenius_projection.py
@@ -1,33 +1,34 @@
 import torch
 from .base_projection import BaseProjection
+from tensordict.nn import TensorDictModule
 from typing import Dict
 
 class FrobeniusProjection(BaseProjection):
-    def __init__(self, in_keys: list[str], out_keys: list[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01, scale_prec: bool = False):
-        super().__init__(in_keys=in_keys, out_keys=out_keys, trust_region_coeff=trust_region_coeff, mean_bound=mean_bound, cov_bound=cov_bound)
+    def __init__(self, in_keys: list[str], out_keys: list[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01, scale_prec: bool = False, contextual_std: bool = True):
+        super().__init__(in_keys=in_keys, out_keys=out_keys, trust_region_coeff=trust_region_coeff, mean_bound=mean_bound, cov_bound=cov_bound, contextual_std=contextual_std)
         self.scale_prec = scale_prec
 
     def project(self, policy_params: Dict[str, torch.Tensor], old_policy_params: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
-        mean, chol = policy_params["loc"], policy_params["scale_tril"]
-        old_mean, old_chol = old_policy_params["loc"], old_policy_params["scale_tril"]
+        mean = policy_params["loc"]
+        old_mean = old_policy_params["loc"]
 
-        cov = torch.matmul(chol, chol.transpose(-1, -2))
-        old_cov = torch.matmul(old_chol, old_chol.transpose(-1, -2))
+        cov = self._calc_covariance(policy_params)
+        old_cov = self._calc_covariance(old_policy_params)
 
         mean_part, cov_part = self._gaussian_frobenius((mean, cov), (old_mean, old_cov))
 
         proj_mean = self._mean_projection(mean, old_mean, mean_part)
         proj_cov = self._cov_projection(cov, old_cov, cov_part)
 
-        proj_chol = torch.linalg.cholesky(proj_cov)
-        return {"loc": proj_mean, "scale_tril": proj_chol}
+        scale_or_scale_tril = self._calc_scale_or_scale_tril(proj_cov)
+        return {"loc": proj_mean, self.out_keys[1]: scale_or_scale_tril}
 
     def get_trust_region_loss(self, policy_params: Dict[str, torch.Tensor], proj_policy_params: Dict[str, torch.Tensor]) -> torch.Tensor:
-        mean, chol = policy_params["loc"], policy_params["scale_tril"]
-        proj_mean, proj_chol = proj_policy_params["loc"], proj_policy_params["scale_tril"]
+        mean = policy_params["loc"]
+        proj_mean = proj_policy_params["loc"]
 
-        cov = torch.matmul(chol, chol.transpose(-1, -2))
-        proj_cov = torch.matmul(proj_chol, proj_chol.transpose(-1, -2))
+        cov = self._calc_covariance(policy_params)
+        proj_cov = self._calc_covariance(proj_policy_params)
 
         mean_diff = torch.sum(torch.square(mean - proj_mean), dim=-1)
         cov_diff = torch.sum(torch.square(cov - proj_cov), dim=(-2, -1))
diff --git a/fancy_rl/projections/identity_projection.py b/fancy_rl/projections/identity_projection.py
index adb8af3..c11c3e9 100644
--- a/fancy_rl/projections/identity_projection.py
+++ b/fancy_rl/projections/identity_projection.py
@@ -3,8 +3,8 @@ from .base_projection import BaseProjection
 from typing import Dict
 
 class IdentityProjection(BaseProjection):
-    def __init__(self, in_keys: list[str], out_keys: list[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01):
-        super().__init__(in_keys=in_keys, out_keys=out_keys, trust_region_coeff=trust_region_coeff, mean_bound=mean_bound, cov_bound=cov_bound)
+    def __init__(self, in_keys: list[str], out_keys: list[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01, contextual_std: bool = True):
+        super().__init__(in_keys=in_keys, out_keys=out_keys, trust_region_coeff=trust_region_coeff, mean_bound=mean_bound, cov_bound=cov_bound, contextual_std=contextual_std)
 
     def project(self, policy_params: Dict[str, torch.Tensor], old_policy_params: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
         return policy_params
diff --git a/fancy_rl/projections/kl_projection.py b/fancy_rl/projections/kl_projection.py
index 4dddecd..eb65fd8 100644
--- a/fancy_rl/projections/kl_projection.py
+++ b/fancy_rl/projections/kl_projection.py
@@ -2,6 +2,7 @@ import torch
 import cpp_projection
 import numpy as np
 from .base_projection import BaseProjection
+from tensordict.nn import TensorDictModule
 from typing import Dict, Tuple, Any
 
 MAX_EVAL = 1000
@@ -10,57 +11,65 @@ def get_numpy(tensor):
     return tensor.detach().cpu().numpy()
 
 class KLProjection(BaseProjection):
-    def __init__(self, in_keys: list[str], out_keys: list[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01, is_diag: bool = True, contextual_std: bool = True):
-        super().__init__(in_keys=in_keys, out_keys=out_keys, trust_region_coeff=trust_region_coeff, mean_bound=mean_bound, cov_bound=cov_bound)
-        self.is_diag = is_diag
-        self.contextual_std = contextual_std
+    def __init__(self, in_keys: list[str], out_keys: list[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01, contextual_std: bool = True):
+        super().__init__(in_keys=in_keys, out_keys=out_keys, trust_region_coeff=trust_region_coeff, mean_bound=mean_bound, cov_bound=cov_bound, contextual_std=contextual_std)
 
     def project(self, policy_params: Dict[str, torch.Tensor], old_policy_params: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
-        mean, std = policy_params["loc"], policy_params["scale_tril"]
-        old_mean, old_std = old_policy_params["loc"], old_policy_params["scale_tril"]
+        mean, scale_or_tril = policy_params["loc"], policy_params[self.in_keys[1]]
+        old_mean, old_scale_or_tril = old_policy_params["loc"], old_policy_params[self.in_keys[1]]
 
-        mean_part, cov_part = self._gaussian_kl((mean, std), (old_mean, old_std))
+        mean_part, cov_part = self._gaussian_kl((mean, scale_or_tril), (old_mean, old_scale_or_tril))
 
         if not self.contextual_std:
-            std = std[:1]
-            old_std = old_std[:1]
+            scale_or_tril = scale_or_tril[:1]
+            old_scale_or_tril = old_scale_or_tril[:1]
             cov_part = cov_part[:1]
 
         proj_mean = self._mean_projection(mean, old_mean, mean_part)
-        proj_std = self._cov_projection(std, old_std, cov_part)
+        proj_scale_or_tril = self._cov_projection(scale_or_tril, old_scale_or_tril, cov_part)
 
         if not self.contextual_std:
-            proj_std = proj_std.expand(mean.shape[0], -1, -1)
+            proj_scale_or_tril = proj_scale_or_tril.expand(mean.shape[0], *proj_scale_or_tril.shape[1:])
 
-        return {"loc": proj_mean, "scale_tril": proj_std}
+        return {"loc": proj_mean, self.out_keys[1]: proj_scale_or_tril}
 
     def get_trust_region_loss(self, policy_params: Dict[str, torch.Tensor], proj_policy_params: Dict[str, torch.Tensor]) -> torch.Tensor:
-        mean, std = policy_params["loc"], policy_params["scale_tril"]
-        proj_mean, proj_std = proj_policy_params["loc"], proj_policy_params["scale_tril"]
-        kl = sum(self._gaussian_kl((mean, std), (proj_mean, proj_std)))
+        mean, scale_or_tril = policy_params["loc"], policy_params[self.in_keys[1]]
+        proj_mean, proj_scale_or_tril = proj_policy_params["loc"], proj_policy_params[self.out_keys[1]]
+        kl = sum(self._gaussian_kl((mean, scale_or_tril), (proj_mean, proj_scale_or_tril)))
         return kl.mean() * self.trust_region_coeff
 
     def _gaussian_kl(self, p: Tuple[torch.Tensor, torch.Tensor], q: Tuple[torch.Tensor, torch.Tensor]) -> Tuple[torch.Tensor, torch.Tensor]:
-        mean, std = p
-        mean_other, std_other = q
+        mean, scale_or_tril = p
+        mean_other, scale_or_tril_other = q
         k = mean.shape[-1]
 
-        maha_part = 0.5 * self._maha(mean, mean_other, std_other)
+        maha_part = 0.5 * self._maha(mean, mean_other, scale_or_tril_other)
 
-        det_term = self._log_determinant(std)
-        det_term_other = self._log_determinant(std_other)
+        det_term = self._log_determinant(scale_or_tril)
+        det_term_other = self._log_determinant(scale_or_tril_other)
+
+        if self.full_cov:
+            trace_part = self._torch_batched_trace_square(torch.linalg.solve_triangular(scale_or_tril_other, scale_or_tril, upper=False))
+        else:
+            trace_part = torch.sum((scale_or_tril / scale_or_tril_other) ** 2, dim=-1)
 
-        trace_part = self._torch_batched_trace_square(torch.linalg.solve_triangular(std_other, std, upper=False))
         cov_part = 0.5 * (trace_part - k + det_term_other - det_term)
 
         return maha_part, cov_part
 
-    def _maha(self, x: torch.Tensor, y: torch.Tensor, std: torch.Tensor) -> torch.Tensor:
+    def _maha(self, x: torch.Tensor, y: torch.Tensor, scale_or_tril: torch.Tensor) -> torch.Tensor:
         diff = x - y
-        return torch.sum(torch.square(torch.triangular_solve(diff.unsqueeze(-1), std, upper=False)[0].squeeze(-1)), dim=-1)
+        if self.full_cov:
+            return torch.sum(torch.square(torch.triangular_solve(diff.unsqueeze(-1), scale_or_tril, upper=False)[0].squeeze(-1)), dim=-1)
+        else:
+            return torch.sum(torch.square(diff / scale_or_tril), dim=-1)
 
-    def _log_determinant(self, std: torch.Tensor) -> torch.Tensor:
-        return 2 * torch.log(std.diagonal(dim1=-2, dim2=-1)).sum(-1)
+    def _log_determinant(self, scale_or_tril: torch.Tensor) -> torch.Tensor:
+        if self.full_cov:
+            return 2 * torch.log(scale_or_tril.diagonal(dim1=-2, dim2=-1)).sum(-1)
+        else:
+            return 2 * torch.log(scale_or_tril).sum(-1)
 
     def _torch_batched_trace_square(self, x: torch.Tensor) -> torch.Tensor:
         return torch.sum(x.pow(2), dim=(-2, -1))
@@ -68,49 +77,45 @@ class KLProjection(BaseProjection):
     def _mean_projection(self, mean: torch.Tensor, old_mean: torch.Tensor, mean_part: torch.Tensor) -> torch.Tensor:
         return old_mean + (mean - old_mean) * torch.sqrt(self.mean_bound / (mean_part + 1e-8)).unsqueeze(-1)
 
-    def _cov_projection(self, std: torch.Tensor, old_std: torch.Tensor, cov_part: torch.Tensor) -> torch.Tensor:
-        cov = torch.matmul(std, std.transpose(-1, -2))
-        old_cov = torch.matmul(old_std, old_std.transpose(-1, -2))
-
-        if self.is_diag:
-            mask = cov_part > self.cov_bound
-            proj_std = torch.zeros_like(std)
-            proj_std[~mask] = std[~mask]
-            try:
-                if mask.any():
-                    proj_cov = KLProjectionGradFunctionDiagCovOnly.apply(cov.diagonal(dim1=-2, dim2=-1),
-                                                                         old_cov.diagonal(dim1=-2, dim2=-1),
-                                                                         self.cov_bound)
-                    is_invalid = (proj_cov.mean(dim=-1).isnan() | proj_cov.mean(dim=-1).isinf() | (proj_cov.min(dim=-1).values < 0)) & mask
-                    if is_invalid.any():
-                        proj_std[is_invalid] = old_std[is_invalid]
-                        mask &= ~is_invalid
-                    proj_std[mask] = proj_cov[mask].sqrt().diag_embed()
-            except Exception as e:
-                proj_std = old_std
+    def _cov_projection(self, scale_or_tril: torch.Tensor, old_scale_or_tril: torch.Tensor, cov_part: torch.Tensor) -> torch.Tensor:
+        if self.full_cov:
+            cov = torch.matmul(scale_or_tril, scale_or_tril.transpose(-1, -2))
+            old_cov = torch.matmul(old_scale_or_tril, old_scale_or_tril.transpose(-1, -2))
         else:
-            try:
-                mask = cov_part > self.cov_bound
-                proj_std = torch.zeros_like(std)
-                proj_std[~mask] = std[~mask]
-                if mask.any():
-                    proj_cov = KLProjectionGradFunctionCovOnly.apply(cov, std.detach(), old_std, self.cov_bound)
+            cov = scale_or_tril.pow(2)
+            old_cov = old_scale_or_tril.pow(2)
+
+        mask = cov_part > self.cov_bound
+        proj_scale_or_tril = torch.zeros_like(scale_or_tril)
+        proj_scale_or_tril[~mask] = scale_or_tril[~mask]
+
+        try:
+            if mask.any():
+                if self.full_cov:
+                    proj_cov = KLProjectionGradFunctionCovOnly.apply(cov, scale_or_tril.detach(), old_scale_or_tril, self.cov_bound)
                     is_invalid = proj_cov.mean([-2, -1]).isnan() & mask
                     if is_invalid.any():
-                        proj_std[is_invalid] = old_std[is_invalid]
+                        proj_scale_or_tril[is_invalid] = old_scale_or_tril[is_invalid]
                         mask &= ~is_invalid
-                    proj_std[mask], failed_mask = torch.linalg.cholesky_ex(proj_cov[mask])
+                    proj_scale_or_tril[mask], failed_mask = torch.linalg.cholesky_ex(proj_cov[mask])
                     failed_mask = failed_mask.bool()
                     if failed_mask.any():
-                        proj_std[failed_mask] = old_std[failed_mask]
-            except Exception as e:
-                import logging
-                logging.error('Projection failed, taking old cholesky for projection.')
-                print("Projection failed, taking old cholesky for projection.")
-                proj_std = old_std
-                raise e
+                        proj_scale_or_tril[failed_mask] = old_scale_or_tril[failed_mask]
+                else:
+                    proj_cov = KLProjectionGradFunctionDiagCovOnly.apply(cov, old_cov, self.cov_bound)
+                    is_invalid = (proj_cov.mean(dim=-1).isnan() | proj_cov.mean(dim=-1).isinf() | (proj_cov.min(dim=-1).values < 0)) & mask
+                    if is_invalid.any():
+                        proj_scale_or_tril[is_invalid] = old_scale_or_tril[is_invalid]
+                        mask &= ~is_invalid
+                    proj_scale_or_tril[mask] = proj_cov[mask].sqrt()
+        except Exception as e:
+            import logging
+            logging.error('Projection failed, taking old scale_or_tril for projection.')
+            print("Projection failed, taking old scale_or_tril for projection.")
+            proj_scale_or_tril = old_scale_or_tril
+            raise e
 
-        return proj_std
+        return proj_scale_or_tril
 
 
 class KLProjectionGradFunctionCovOnly(torch.autograd.Function):
diff --git a/fancy_rl/projections/wasserstein_projection.py b/fancy_rl/projections/wasserstein_projection.py
index fb58058..d19dc84 100644
--- a/fancy_rl/projections/wasserstein_projection.py
+++ b/fancy_rl/projections/wasserstein_projection.py
@@ -1,56 +1,86 @@
 import torch
 from .base_projection import BaseProjection
+from tensordict.nn import TensorDictModule
 from typing import Dict, Tuple
 
+def scale_tril_to_sqrt(scale_tril: torch.Tensor) -> torch.Tensor:
+    """
+    'Converts' scale_tril to scale_sqrt.
+    
+    For Wasserstein distance, we need the matrix square root, not the Cholesky decomposition.
+    But since both are lower triangular, we can treat the Cholesky decomposition as if it were the matrix square root.
+    """
+    return scale_tril
+
 def gaussian_wasserstein_commutative(policy, p: Tuple[torch.Tensor, torch.Tensor],
                                      q: Tuple[torch.Tensor, torch.Tensor], scale_prec=False) -> Tuple[torch.Tensor, torch.Tensor]:
-    mean, sqrt = p
-    mean_other, sqrt_other = q
+    mean, scale_or_sqrt = p
+    mean_other, scale_or_sqrt_other = q
 
     mean_part = torch.sum(torch.square(mean - mean_other), dim=-1)
 
-    cov = torch.matmul(sqrt, sqrt.transpose(-1, -2))
-    cov_other = torch.matmul(sqrt_other, sqrt_other.transpose(-1, -2))
-
-    if scale_prec:
-        identity = torch.eye(mean.shape[-1], dtype=sqrt.dtype, device=sqrt.device)
-        sqrt_inv_other = torch.linalg.solve(sqrt_other, identity)
-        c = sqrt_inv_other @ cov @ sqrt_inv_other
-        cov_part = torch.trace(identity + c - 2 * sqrt_inv_other @ sqrt)
-    else:
-        cov_part = torch.trace(cov_other + cov - 2 * sqrt_other @ sqrt)
+    if scale_or_sqrt.dim() == mean.dim():  # Diagonal case
+        cov = scale_or_sqrt.pow(2)
+        cov_other = scale_or_sqrt_other.pow(2)
+        if scale_prec:
+            identity = torch.eye(mean.shape[-1], dtype=scale_or_sqrt.dtype, device=scale_or_sqrt.device)
+            sqrt_inv_other = 1 / scale_or_sqrt_other
+            c = sqrt_inv_other.pow(2) * cov
+            cov_part = torch.sum(identity + c - 2 * sqrt_inv_other * scale_or_sqrt, dim=-1)
+        else:
+            cov_part = torch.sum(cov_other + cov - 2 * scale_or_sqrt_other * scale_or_sqrt, dim=-1)
+    else:  # Full covariance case
+        # Note: scale_or_sqrt is treated as the matrix square root, not Cholesky decomposition
+        cov = torch.matmul(scale_or_sqrt, scale_or_sqrt.transpose(-1, -2))
+        cov_other = torch.matmul(scale_or_sqrt_other, scale_or_sqrt_other.transpose(-1, -2))
+        if scale_prec:
+            identity = torch.eye(mean.shape[-1], dtype=scale_or_sqrt.dtype, device=scale_or_sqrt.device)
+            sqrt_inv_other = torch.linalg.solve(scale_or_sqrt_other, identity)
+            c = sqrt_inv_other @ cov @ sqrt_inv_other.transpose(-1, -2)
+            cov_part = torch.trace(identity + c - 2 * sqrt_inv_other @ scale_or_sqrt)
+        else:
+            cov_part = torch.trace(cov_other + cov - 2 * scale_or_sqrt_other @ scale_or_sqrt)
 
     return mean_part, cov_part
 
 class WassersteinProjection(BaseProjection):
-    def __init__(self, in_keys: list[str], out_keys: list[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01, scale_prec: bool = False):
-        super().__init__(in_keys=in_keys, out_keys=out_keys, trust_region_coeff=trust_region_coeff, mean_bound=mean_bound, cov_bound=cov_bound)
+    def __init__(self, in_keys: list[str], out_keys: list[str], trust_region_coeff: float = 1.0, mean_bound: float = 0.01, cov_bound: float = 0.01, scale_prec: bool = False, contextual_std: bool = True):
+        super().__init__(in_keys=in_keys, out_keys=out_keys, trust_region_coeff=trust_region_coeff, mean_bound=mean_bound, cov_bound=cov_bound, contextual_std=contextual_std)
         self.scale_prec = scale_prec
 
     def project(self, policy_params: Dict[str, torch.Tensor], old_policy_params: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
-        mean, sqrt = policy_params["loc"], policy_params["scale_tril"]
-        old_mean, old_sqrt = old_policy_params["loc"], old_policy_params["scale_tril"]
+        mean = policy_params["loc"]
+        old_mean = old_policy_params["loc"]
+        scale_or_sqrt = scale_tril_to_sqrt(policy_params[self.in_keys[1]])
+        old_scale_or_sqrt = scale_tril_to_sqrt(old_policy_params[self.in_keys[1]])
 
-        mean_part, cov_part = gaussian_wasserstein_commutative(None, (mean, sqrt), (old_mean, old_sqrt), self.scale_prec)
+        mean_part, cov_part = gaussian_wasserstein_commutative(None, (mean, scale_or_sqrt), (old_mean, old_scale_or_sqrt), self.scale_prec)
 
         proj_mean = self._mean_projection(mean, old_mean, mean_part)
-        proj_sqrt = self._cov_projection(sqrt, old_sqrt, cov_part)
+        proj_scale_or_sqrt = self._cov_projection(scale_or_sqrt, old_scale_or_sqrt, cov_part)
 
-        return {"loc": proj_mean, "scale_tril": proj_sqrt}
+        return {"loc": proj_mean, self.out_keys[1]: proj_scale_or_sqrt}
 
     def get_trust_region_loss(self, policy_params: Dict[str, torch.Tensor], proj_policy_params: Dict[str, torch.Tensor]) -> torch.Tensor:
-        mean, sqrt = policy_params["loc"], policy_params["scale_tril"]
-        proj_mean, proj_sqrt = proj_policy_params["loc"], proj_policy_params["scale_tril"]
-        mean_part, cov_part = gaussian_wasserstein_commutative(None, (mean, sqrt), (proj_mean, proj_sqrt), self.scale_prec)
+        mean = policy_params["loc"]
+        proj_mean = proj_policy_params["loc"]
+        scale_or_sqrt = scale_tril_to_sqrt(policy_params[self.in_keys[1]])
+        proj_scale_or_sqrt = scale_tril_to_sqrt(proj_policy_params[self.out_keys[1]])
+        mean_part, cov_part = gaussian_wasserstein_commutative(None, (mean, scale_or_sqrt), (proj_mean, proj_scale_or_sqrt), self.scale_prec)
         w2 = mean_part + cov_part
         return w2.mean() * self.trust_region_coeff
 
     def _mean_projection(self, mean: torch.Tensor, old_mean: torch.Tensor, mean_part: torch.Tensor) -> torch.Tensor:
         diff = mean - old_mean
-        norm = torch.norm(diff, dim=-1, keepdim=True)
-        return torch.where(norm > self.mean_bound, old_mean + diff * self.mean_bound / norm, mean)
+        norm = torch.sqrt(mean_part)
+        return torch.where(norm > self.mean_bound, old_mean + diff * self.mean_bound / norm.unsqueeze(-1), mean)
 
-    def _cov_projection(self, sqrt: torch.Tensor, old_sqrt: torch.Tensor, cov_part: torch.Tensor) -> torch.Tensor:
-        diff = sqrt - old_sqrt
-        norm = torch.norm(diff, dim=(-2, -1), keepdim=True)
-        return torch.where(norm > self.cov_bound, old_sqrt + diff * self.cov_bound / norm, sqrt)
\ No newline at end of file
+    def _cov_projection(self, scale_or_sqrt: torch.Tensor, old_scale_or_sqrt: torch.Tensor, cov_part: torch.Tensor) -> torch.Tensor:
+        if scale_or_sqrt.dim() == old_scale_or_sqrt.dim() == 2:  # Diagonal case
+            diff = scale_or_sqrt - old_scale_or_sqrt
+            norm = torch.sqrt(cov_part)
+            return torch.where(norm > self.cov_bound, old_scale_or_sqrt + diff * self.cov_bound / norm.unsqueeze(-1), scale_or_sqrt)
+        else:  # Full covariance case
+            diff = scale_or_sqrt - old_scale_or_sqrt
+            norm = torch.norm(diff, dim=(-2, -1), keepdim=True)
+            return torch.where(norm > self.cov_bound, old_scale_or_sqrt + diff * self.cov_bound / norm, scale_or_sqrt)
\ No newline at end of file