diff --git a/docs/misc/changelog.rst b/docs/misc/changelog.rst
index 5999aa9c7..78d42eba3 100644
--- a/docs/misc/changelog.rst
+++ b/docs/misc/changelog.rst
@@ -3,7 +3,7 @@
 Changelog
 ==========
 
-Release 2.2.0a9 (WIP)
+Release 2.2.0a10 (WIP)
 --------------------------
 **Support for options at reset, bug fixes and better error messages**
 
@@ -59,6 +59,7 @@ Others:
 - Buffers do no call an additional ``.copy()`` when storing new transitions
 - Fixed ``ActorCriticPolicy.extract_features()`` signature by adding an optional ``features_extractor`` argument
 - Update dependencies (accept newer Shimmy/Sphinx version and remove ``sphinx_autodoc_typehints``)
+- Fixed ``stable_baselines3/common/distributions.py`` type hints
 
 Documentation:
 ^^^^^^^^^^^^^^
diff --git a/pyproject.toml b/pyproject.toml
index 2d0c61914..9476868c4 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -35,7 +35,8 @@ exclude = [
   "stable_baselines3/common/on_policy_algorithm.py",
   "stable_baselines3/common/vec_env/stacked_observations.py",
   "stable_baselines3/common/vec_env/subproc_vec_env.py",
-  "stable_baselines3/common/vec_env/patch_gym.py"
+  "stable_baselines3/common/vec_env/patch_gym.py",
+  "stable_baselines3/common/distributions.py",
 ]
 
 [tool.mypy]
@@ -43,8 +44,7 @@ ignore_missing_imports = true
 follow_imports = "silent"
 show_error_codes = true
 exclude = """(?x)(
-    stable_baselines3/common/distributions.py$
-    | stable_baselines3/common/off_policy_algorithm.py$
+    stable_baselines3/common/off_policy_algorithm.py$
     | stable_baselines3/common/policies.py$
     | stable_baselines3/common/vec_env/__init__.py$
     | stable_baselines3/common/vec_env/vec_normalize.py$
diff --git a/stable_baselines3/common/distributions.py b/stable_baselines3/common/distributions.py
index 8a8e9f903..149345d83 100644
--- a/stable_baselines3/common/distributions.py
+++ b/stable_baselines3/common/distributions.py
@@ -175,7 +175,7 @@ def log_prob(self, actions: th.Tensor) -> th.Tensor:
         log_prob = self.distribution.log_prob(actions)
         return sum_independent_dims(log_prob)
 
-    def entropy(self) -> th.Tensor:
+    def entropy(self) -> Optional[th.Tensor]:
         return sum_independent_dims(self.distribution.entropy())
 
     def sample(self) -> th.Tensor:
@@ -216,7 +216,7 @@ def __init__(self, action_dim: int, epsilon: float = 1e-6):
         super().__init__(action_dim)
         # Avoid NaN (prevents division by zero or log of zero)
         self.epsilon = epsilon
-        self.gaussian_actions = None
+        self.gaussian_actions: Optional[th.Tensor] = None
 
     def proba_distribution(
         self: SelfSquashedDiagGaussianDistribution, mean_actions: th.Tensor, log_std: th.Tensor
@@ -339,7 +339,7 @@ def proba_distribution_net(self, latent_dim: int) -> nn.Module:
     def proba_distribution(
         self: SelfMultiCategoricalDistribution, action_logits: th.Tensor
     ) -> SelfMultiCategoricalDistribution:
-        self.distribution = [Categorical(logits=split) for split in th.split(action_logits, tuple(self.action_dims), dim=1)]
+        self.distribution = [Categorical(logits=split) for split in th.split(action_logits, list(self.action_dims), dim=1)]
         return self
 
     def log_prob(self, actions: th.Tensor) -> th.Tensor:
@@ -440,6 +440,13 @@ class StateDependentNoiseDistribution(Distribution):
     :param epsilon: small value to avoid NaN due to numerical imprecision.
     """
 
+    bijector: Optional["TanhBijector"]
+    latent_sde_dim: Optional[int]
+    weights_dist: Normal
+    _latent_sde: th.Tensor
+    exploration_mat: th.Tensor
+    exploration_matrices: th.Tensor
+
     def __init__(
         self,
         action_dim: int,
@@ -454,10 +461,6 @@ def __init__(
         self.latent_sde_dim = None
         self.mean_actions = None
         self.log_std = None
-        self.weights_dist = None
-        self.exploration_mat = None
-        self.exploration_matrices = None
-        self._latent_sde = None
         self.use_expln = use_expln
         self.full_std = full_std
         self.epsilon = epsilon
@@ -489,6 +492,7 @@ def get_std(self, log_std: th.Tensor) -> th.Tensor:
 
         if self.full_std:
             return std
+        assert self.latent_sde_dim is not None
         # Reduce the number of parameters:
         return th.ones(self.latent_sde_dim, self.action_dim).to(log_std.device) * std
 
@@ -675,10 +679,13 @@ def make_proba_distribution(
         cls = StateDependentNoiseDistribution if use_sde else DiagGaussianDistribution
         return cls(get_action_dim(action_space), **dist_kwargs)
     elif isinstance(action_space, spaces.Discrete):
-        return CategoricalDistribution(action_space.n, **dist_kwargs)
+        return CategoricalDistribution(int(action_space.n), **dist_kwargs)
     elif isinstance(action_space, spaces.MultiDiscrete):
         return MultiCategoricalDistribution(list(action_space.nvec), **dist_kwargs)
     elif isinstance(action_space, spaces.MultiBinary):
+        assert isinstance(
+            action_space.n, int
+        ), f"Multi-dimensional MultiBinary({action_space.n}) action space is not supported. You can flatten it instead."
         return BernoulliDistribution(action_space.n, **dist_kwargs)
     else:
         raise NotImplementedError(
@@ -702,7 +709,10 @@ def kl_divergence(dist_true: Distribution, dist_pred: Distribution) -> th.Tensor
     # MultiCategoricalDistribution is not a PyTorch Distribution subclass
     # so we need to implement it ourselves!
     if isinstance(dist_pred, MultiCategoricalDistribution):
-        assert np.allclose(dist_pred.action_dims, dist_true.action_dims), "Error: distributions must have the same input space"
+        assert isinstance(dist_true, MultiCategoricalDistribution)  # already checked above, for mypy
+        assert np.allclose(
+            dist_pred.action_dims, dist_true.action_dims
+        ), f"Error: distributions must have the same input space: {dist_pred.action_dims} != {dist_true.action_dims}"
         return th.stack(
             [th.distributions.kl_divergence(p, q) for p, q in zip(dist_true.distribution, dist_pred.distribution)],
             dim=1,
diff --git a/stable_baselines3/common/preprocessing.py b/stable_baselines3/common/preprocessing.py
index a2d0e59c1..2b5251cf8 100644
--- a/stable_baselines3/common/preprocessing.py
+++ b/stable_baselines3/common/preprocessing.py
@@ -204,7 +204,7 @@ def get_action_dim(action_space: spaces.Space) -> int:
         # Number of binary actions
         assert isinstance(
             action_space.n, int
-        ), "Multi-dimensional MultiBinary action space is not supported. You can flatten it instead."
+        ), f"Multi-dimensional MultiBinary({action_space.n}) action space is not supported. You can flatten it instead."
         return int(action_space.n)
     else:
         raise NotImplementedError(f"{action_space} action space is not supported")
diff --git a/stable_baselines3/version.txt b/stable_baselines3/version.txt
index b7120ad62..b208680f4 100644
--- a/stable_baselines3/version.txt
+++ b/stable_baselines3/version.txt
@@ -1 +1 @@
-2.2.0a9
+2.2.0a10
diff --git a/tests/test_spaces.py b/tests/test_spaces.py
index e4a933976..e006c1f96 100644
--- a/tests/test_spaces.py
+++ b/tests/test_spaces.py
@@ -168,3 +168,9 @@ def test_float64_action_space(model_class, obs_space, action_space):
     initial_obs, _ = env.reset()
     action, _ = model.predict(initial_obs, deterministic=False)
     assert action.dtype == env.action_space.dtype
+
+
+def test_multidim_binary_not_supported():
+    env = DummyEnv(BOX_SPACE_FLOAT32, spaces.MultiBinary([2, 3]))
+    with pytest.raises(AssertionError, match=r"Multi-dimensional MultiBinary\(.*\) action space is not supported"):
+        A2C("MlpPolicy", env)