diff --git a/tests/test_regression.py b/tests/test_regression.py
index 5d3b8f65..3ffcf99e 100644
--- a/tests/test_regression.py
+++ b/tests/test_regression.py
@@ -1,79 +1,31 @@
+from pathlib import Path
+
 import pytest
 import torch
+from safetensors.torch import load_file
 
-from lerobot.common.datasets.factory import make_dataset
-from lerobot.common.policies.factory import make_policy
-from lerobot.common.utils.utils import init_hydra_config, set_global_seed
-from lerobot.scripts.train import make_optimizer
-from tests.utils import DEFAULT_CONFIG_PATH, DEVICE, require_env
+from tests.scripts.save_policy_to_safetensor import get_policy_stats
 
 
 @pytest.mark.parametrize(
-    "env_name,policy_name,extra_overrides",
+    "env_name,policy_name",
     [
-        # ("xarm", "tdmpc", ["policy.mpc=true"]),
-        # ("pusht", "tdmpc", ["policy.mpc=false"]),
-        ("pusht", "diffusion", []),
+        # ("xarm", "tdmpc"),
+        ("pusht", "diffusion"),
         ("aloha", "act"),
     ],
 )
-@require_env
 def test_backward_compatibility(env_name, policy_name):
-    cfg = init_hydra_config(
-        DEFAULT_CONFIG_PATH,
-        overrides=[
-            f"env={env_name}",
-            f"policy={policy_name}",
-            f"device={DEVICE}",
-        ],
-    )
-    set_global_seed(1337)
-    dataset = make_dataset(cfg)
-    policy = make_policy(cfg, dataset_stats=dataset.stats)
-    policy.train()
-    policy.to(DEVICE)
-    optimizer, _ = make_optimizer(cfg, policy)
+    env_policy_dir = Path("tests/data/save_policy_to_safetensors") / f"{env_name}_{policy_name}"
+    saved_grad_stats = load_file(env_policy_dir / "grad_stats")
+    saved_param_stats = load_file(env_policy_dir / "param_stats")
+    saved_actions = load_file(env_policy_dir / "actions")
 
-    dataloader = torch.utils.data.DataLoader(
-        dataset,
-        num_workers=0,
-        batch_size=cfg.training.batch_size,
-        shuffle=False,
-    )
+    grad_stats, param_stats, actions = get_policy_stats(env_name, policy_name)
 
-    batch = next(iter(dataloader))
-    output_dict = policy.forward(batch)
-    loss = output_dict["loss"]
-    # TODO Check output dict values
-
-    loss.backward()
-    grad_stats = {}
-    for key, param in policy.named_parameters():
-        if param.requires_grad:
-            grad_stats[f"{key}_mean"] = param.grad.mean()
-            grad_stats[f"{key}_std"] = param.grad.std()
-
-    optimizer.step()
-    param_stats = {}
-    for key, param in policy.named_parameters():
-        param_stats[f"{key}_mean"] = param.mean()
-        param_stats[f"{key}_std"] = param.std()
-
-    optimizer.zero_grad()
-    policy.reset()
-
-    dataset.delta_timestamps = None
-    batch = next(iter(dataloader))
-
-    # TODO(aliberts): refacor `select_action` methods so that it expects `obs` instead of `batch`
-    if policy_name == "diffusion":
-        batch = {k: batch[k] for k in ["observation.image", "observation.state"]}
-
-    actions = {i: policy.select_action(batch) for i in range(cfg.policy.n_action_steps)}
-
-    print(len(actions))
-
-
-if __name__ == "__main__":
-    # test_backward_compatibility("aloha", "act")
-    test_backward_compatibility("pusht", "diffusion")
+    for key in saved_grad_stats:
+        assert torch.isclose(grad_stats[key], saved_grad_stats[key]).all()
+    for key in saved_param_stats:
+        assert torch.isclose(param_stats[key], saved_param_stats[key]).all()
+    for key in saved_actions:
+        assert torch.isclose(actions[key], saved_actions[key]).all()