diff --git a/lerobot/common/policies/tdmpc/modeling_tdmpc.py b/lerobot/common/policies/tdmpc/modeling_tdmpc.py
index eab0f94e..1fba43d0 100644
--- a/lerobot/common/policies/tdmpc/modeling_tdmpc.py
+++ b/lerobot/common/policies/tdmpc/modeling_tdmpc.py
@@ -80,7 +80,8 @@ class TDMPCPolicy(nn.Module, PyTorchModelHubMixin):
         self.config = config
         self.model = TDMPCTOLD(config)
         self.model_target = deepcopy(self.model)
-        self.model_target.eval()
+        for param in self.model_target.parameters():
+            param.requires_grad = False
 
         if config.input_normalization_modes is not None:
             self.normalize_inputs = Normalize(
diff --git a/lerobot/configs/policy/tdmpc.yaml b/lerobot/configs/policy/tdmpc.yaml
index 71dfa9c9..eb89033b 100644
--- a/lerobot/configs/policy/tdmpc.yaml
+++ b/lerobot/configs/policy/tdmpc.yaml
@@ -1,6 +1,7 @@
 # @package _global_
 
 seed: 1
+dataset_repo_id: lerobot/xarm_lift_medium_replay
 
 training:
   offline_steps: 25000
diff --git a/lerobot/scripts/train.py b/lerobot/scripts/train.py
index 268185a3..f58dbd06 100644
--- a/lerobot/scripts/train.py
+++ b/lerobot/scripts/train.py
@@ -25,6 +25,51 @@ from lerobot.common.utils.utils import (
 from lerobot.scripts.eval import eval_policy
 
 
+def make_optimizer_and_scheduler(cfg, policy):
+    if cfg.policy.name == "act":
+        optimizer_params_dicts = [
+            {
+                "params": [
+                    p
+                    for n, p in policy.named_parameters()
+                    if not n.startswith("backbone") and p.requires_grad
+                ]
+            },
+            {
+                "params": [
+                    p for n, p in policy.named_parameters() if n.startswith("backbone") and p.requires_grad
+                ],
+                "lr": cfg.training.lr_backbone,
+            },
+        ]
+        optimizer = torch.optim.AdamW(
+            optimizer_params_dicts, lr=cfg.training.lr, weight_decay=cfg.training.weight_decay
+        )
+        lr_scheduler = None
+    elif cfg.policy.name == "diffusion":
+        optimizer = torch.optim.Adam(
+            policy.diffusion.parameters(),
+            cfg.training.lr,
+            cfg.training.adam_betas,
+            cfg.training.adam_eps,
+            cfg.training.adam_weight_decay,
+        )
+        assert cfg.training.online_steps == 0, "Diffusion Policy does not handle online training."
+        lr_scheduler = get_scheduler(
+            cfg.training.lr_scheduler,
+            optimizer=optimizer,
+            num_warmup_steps=cfg.training.lr_warmup_steps,
+            num_training_steps=cfg.training.offline_steps,
+        )
+    elif policy.name == "tdmpc":
+        optimizer = torch.optim.Adam(policy.parameters(), cfg.training.lr)
+        lr_scheduler = None
+    else:
+        raise NotImplementedError()
+
+    return optimizer, lr_scheduler
+
+
 def update_policy(policy, batch, optimizer, grad_clip_norm, lr_scheduler=None):
     start_time = time.time()
     policy.train()
@@ -276,46 +321,7 @@ def train(cfg: dict, out_dir=None, job_name=None):
 
     # Create optimizer and scheduler
     # Temporary hack to move optimizer out of policy
-    if cfg.policy.name == "act":
-        optimizer_params_dicts = [
-            {
-                "params": [
-                    p
-                    for n, p in policy.named_parameters()
-                    if not n.startswith("backbone") and p.requires_grad
-                ]
-            },
-            {
-                "params": [
-                    p for n, p in policy.named_parameters() if n.startswith("backbone") and p.requires_grad
-                ],
-                "lr": cfg.training.lr_backbone,
-            },
-        ]
-        optimizer = torch.optim.AdamW(
-            optimizer_params_dicts, lr=cfg.training.lr, weight_decay=cfg.training.weight_decay
-        )
-        lr_scheduler = None
-    elif cfg.policy.name == "diffusion":
-        optimizer = torch.optim.Adam(
-            policy.diffusion.parameters(),
-            cfg.training.lr,
-            cfg.training.adam_betas,
-            cfg.training.adam_eps,
-            cfg.training.adam_weight_decay,
-        )
-        assert cfg.training.online_steps == 0, "Diffusion Policy does not handle online training."
-        lr_scheduler = get_scheduler(
-            cfg.training.lr_scheduler,
-            optimizer=optimizer,
-            num_warmup_steps=cfg.training.lr_warmup_steps,
-            num_training_steps=cfg.training.offline_steps,
-        )
-    elif policy.name == "tdmpc":
-        optimizer = torch.optim.Adam(policy.parameters(), cfg.training.lr)
-        lr_scheduler = None
-    else:
-        raise NotImplementedError()
+    optimizer, lr_scheduler = make_optimizer_and_scheduler(cfg, policy)
 
     num_learnable_params = sum(p.numel() for p in policy.parameters() if p.requires_grad)
     num_total_params = sum(p.numel() for p in policy.parameters())
diff --git a/tests/data/save_policy_to_safetensors/aloha_act/actions.safetensors b/tests/data/save_policy_to_safetensors/aloha_act/actions.safetensors
new file mode 100644
index 00000000..70c9b6d8
Binary files /dev/null and b/tests/data/save_policy_to_safetensors/aloha_act/actions.safetensors differ
diff --git a/tests/data/save_policy_to_safetensors/aloha_act/grad_stats.safetensors b/tests/data/save_policy_to_safetensors/aloha_act/grad_stats.safetensors
new file mode 100644
index 00000000..2e845189
Binary files /dev/null and b/tests/data/save_policy_to_safetensors/aloha_act/grad_stats.safetensors differ
diff --git a/tests/data/save_policy_to_safetensors/aloha_act/output_dict.safetensors b/tests/data/save_policy_to_safetensors/aloha_act/output_dict.safetensors
new file mode 100644
index 00000000..e8d537c8
Binary files /dev/null and b/tests/data/save_policy_to_safetensors/aloha_act/output_dict.safetensors differ
diff --git a/tests/data/save_policy_to_safetensors/aloha_act/param_stats.safetensors b/tests/data/save_policy_to_safetensors/aloha_act/param_stats.safetensors
new file mode 100644
index 00000000..6e33879f
Binary files /dev/null and b/tests/data/save_policy_to_safetensors/aloha_act/param_stats.safetensors differ
diff --git a/tests/data/save_policy_to_safetensors/pusht_diffusion/actions.safetensors b/tests/data/save_policy_to_safetensors/pusht_diffusion/actions.safetensors
new file mode 100644
index 00000000..d9b20317
Binary files /dev/null and b/tests/data/save_policy_to_safetensors/pusht_diffusion/actions.safetensors differ
diff --git a/tests/data/save_policy_to_safetensors/pusht_diffusion/grad_stats.safetensors b/tests/data/save_policy_to_safetensors/pusht_diffusion/grad_stats.safetensors
new file mode 100644
index 00000000..4eed4aaf
Binary files /dev/null and b/tests/data/save_policy_to_safetensors/pusht_diffusion/grad_stats.safetensors differ
diff --git a/tests/data/save_policy_to_safetensors/pusht_diffusion/output_dict.safetensors b/tests/data/save_policy_to_safetensors/pusht_diffusion/output_dict.safetensors
new file mode 100644
index 00000000..77472bb5
Binary files /dev/null and b/tests/data/save_policy_to_safetensors/pusht_diffusion/output_dict.safetensors differ
diff --git a/tests/data/save_policy_to_safetensors/pusht_diffusion/param_stats.safetensors b/tests/data/save_policy_to_safetensors/pusht_diffusion/param_stats.safetensors
new file mode 100644
index 00000000..a26868db
Binary files /dev/null and b/tests/data/save_policy_to_safetensors/pusht_diffusion/param_stats.safetensors differ
diff --git a/tests/scripts/save_policy_to_safetensor.py b/tests/scripts/save_policy_to_safetensor.py
new file mode 100644
index 00000000..70337c17
--- /dev/null
+++ b/tests/scripts/save_policy_to_safetensor.py
@@ -0,0 +1,101 @@
+import shutil
+from pathlib import Path
+
+import torch
+from safetensors.torch import save_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_and_scheduler
+from tests.utils import DEFAULT_CONFIG_PATH
+
+
+def get_policy_stats(env_name, policy_name, extra_overrides=None):
+    cfg = init_hydra_config(
+        DEFAULT_CONFIG_PATH,
+        overrides=[
+            f"env={env_name}",
+            f"policy={policy_name}",
+            "device=cpu",
+        ]
+        + extra_overrides,
+    )
+    set_global_seed(1337)
+    dataset = make_dataset(cfg)
+    policy = make_policy(cfg, dataset_stats=dataset.stats)
+    policy.train()
+    optimizer, _ = make_optimizer_and_scheduler(cfg, policy)
+
+    dataloader = torch.utils.data.DataLoader(
+        dataset,
+        num_workers=0,
+        batch_size=cfg.training.batch_size,
+        shuffle=False,
+    )
+
+    batch = next(iter(dataloader))
+    output_dict = policy.forward(batch)
+    output_dict = {k: v for k, v in output_dict.items() if isinstance(v, torch.Tensor)}
+    loss = output_dict["loss"]
+
+    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() if param.grad.numel() > 1 else torch.tensor(float(0.0))
+            )
+
+    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() if param.numel() > 1 else torch.tensor(float(0.0))
+
+    optimizer.zero_grad()
+    policy.reset()
+
+    # HACK: We reload a batch with no delta_timestamps as `select_action` won't expect a timestamps dimension
+    dataset.delta_timestamps = None
+    batch = next(iter(dataloader))
+    obs = {
+        k: batch[k]
+        for k in batch
+        if k in ["observation.image", "observation.images.top", "observation.state"]
+    }
+
+    actions_queue = (
+        cfg.policy.n_action_steps if "n_action_steps" in cfg.policy else cfg.policy.n_action_repeats
+    )
+    actions = {str(i): policy.select_action(obs).contiguous() for i in range(actions_queue)}
+    return output_dict, grad_stats, param_stats, actions
+
+
+def save_policy_to_safetensors(output_dir, env_name, policy_name, extra_overrides):
+    env_policy_dir = Path(output_dir) / f"{env_name}_{policy_name}"
+
+    if env_policy_dir.exists():
+        shutil.rmtree(env_policy_dir)
+
+    env_policy_dir.mkdir(parents=True, exist_ok=True)
+    output_dict, grad_stats, param_stats, actions = get_policy_stats(env_name, policy_name, extra_overrides)
+    save_file(output_dict, env_policy_dir / "output_dict.safetensors")
+    save_file(grad_stats, env_policy_dir / "grad_stats.safetensors")
+    save_file(param_stats, env_policy_dir / "param_stats.safetensors")
+    save_file(actions, env_policy_dir / "actions.safetensors")
+
+
+if __name__ == "__main__":
+    env_policies = [
+        # ("xarm", "tdmpc", ["policy.n_action_repeats=2"]),
+        (
+            "pusht",
+            "diffusion",
+            ["policy.n_action_steps=8", "policy.num_inference_steps=10", "policy.down_dims=[128, 256, 512]"],
+        ),
+        ("aloha", "act", ["policy.n_action_steps=10"]),
+    ]
+    for env, policy, extra_overrides in env_policies:
+        save_policy_to_safetensors("tests/data/save_policy_to_safetensors", env, policy, extra_overrides)
diff --git a/tests/test_datasets.py b/tests/test_datasets.py
index e50d4108..22b271be 100644
--- a/tests/test_datasets.py
+++ b/tests/test_datasets.py
@@ -265,7 +265,7 @@ def test_backward_compatibility(repo_id):
 
         for key in new_frame:
             assert torch.isclose(
-                new_frame[key], old_frame[key], rtol=1e-05, atol=1e-08
+                new_frame[key], old_frame[key]
             ).all(), f"{key=} for index={i} does not contain the same value"
 
     # test2 first frames of first episode
diff --git a/tests/test_policies.py b/tests/test_policies.py
index 51cdb93e..7d2f19ba 100644
--- a/tests/test_policies.py
+++ b/tests/test_policies.py
@@ -1,8 +1,10 @@
 import inspect
+from pathlib import Path
 
 import pytest
 import torch
 from huggingface_hub import PyTorchModelHubMixin
+from safetensors.torch import load_file
 
 from lerobot import available_policies
 from lerobot.common.datasets.factory import make_dataset
@@ -13,7 +15,8 @@ from lerobot.common.policies.factory import get_policy_and_config_classes, make_
 from lerobot.common.policies.normalize import Normalize, Unnormalize
 from lerobot.common.policies.policy_protocol import Policy
 from lerobot.common.utils.utils import init_hydra_config
-from tests.utils import DEFAULT_CONFIG_PATH, DEVICE, require_env
+from tests.scripts.save_policy_to_safetensor import get_policy_stats
+from tests.utils import DEFAULT_CONFIG_PATH, DEVICE, require_env, require_x86_64_kernel
 
 
 @pytest.mark.parametrize("policy_name", available_policies)
@@ -228,3 +231,37 @@ def test_normalize(insert_temporal_dim):
     new_unnormalize = Unnormalize(output_shapes, unnormalize_output_modes, stats=None)
     new_unnormalize.load_state_dict(unnormalize.state_dict())
     unnormalize(output_batch)
+
+
+@pytest.mark.parametrize(
+    "env_name, policy_name, extra_overrides",
+    [
+        # ("xarm", "tdmpc", ["policy.n_action_repeats=2"]),
+        (
+            "pusht",
+            "diffusion",
+            ["policy.n_action_steps=8", "policy.num_inference_steps=10", "policy.down_dims=[128, 256, 512]"],
+        ),
+        ("aloha", "act", ["policy.n_action_steps=10"]),
+    ],
+)
+# As artifacts have been generated on an x86_64 kernel, this test won't
+# pass if it's run on another platform due to floating point errors
+@require_x86_64_kernel
+def test_backward_compatibility(env_name, policy_name, extra_overrides):
+    env_policy_dir = Path("tests/data/save_policy_to_safetensors") / f"{env_name}_{policy_name}"
+    saved_output_dict = load_file(env_policy_dir / "output_dict.safetensors")
+    saved_grad_stats = load_file(env_policy_dir / "grad_stats.safetensors")
+    saved_param_stats = load_file(env_policy_dir / "param_stats.safetensors")
+    saved_actions = load_file(env_policy_dir / "actions.safetensors")
+
+    output_dict, grad_stats, param_stats, actions = get_policy_stats(env_name, policy_name, extra_overrides)
+
+    for key in saved_output_dict:
+        assert torch.isclose(output_dict[key], saved_output_dict[key], rtol=0.1, atol=1e-7).all()
+    for key in saved_grad_stats:
+        assert torch.isclose(grad_stats[key], saved_grad_stats[key], rtol=0.1, atol=1e-7).all()
+    for key in saved_param_stats:
+        assert torch.isclose(param_stats[key], saved_param_stats[key], rtol=50, atol=1e-7).all()
+    for key in saved_actions:
+        assert torch.isclose(actions[key], saved_actions[key], rtol=0.1, atol=1e-7).all()
diff --git a/tests/utils.py b/tests/utils.py
index f3fe5790..6a706694 100644
--- a/tests/utils.py
+++ b/tests/utils.py
@@ -1,3 +1,5 @@
+import platform
+
 import pytest
 import torch
 
@@ -9,6 +11,51 @@ DEFAULT_CONFIG_PATH = "lerobot/configs/default.yaml"
 DEVICE = "cuda" if torch.cuda.is_available() else "cpu"
 
 
+def require_x86_64_kernel(func):
+    """
+    Decorator that skips the test if plateform device is not an x86_64 cpu.
+    """
+    from functools import wraps
+
+    @wraps(func)
+    def wrapper(*args, **kwargs):
+        if platform.machine() != "x86_64":
+            pytest.skip("requires x86_64 plateform")
+        return func(*args, **kwargs)
+
+    return wrapper
+
+
+def require_cpu(func):
+    """
+    Decorator that skips the test if device is not cpu.
+    """
+    from functools import wraps
+
+    @wraps(func)
+    def wrapper(*args, **kwargs):
+        if DEVICE != "cpu":
+            pytest.skip("requires cpu")
+        return func(*args, **kwargs)
+
+    return wrapper
+
+
+def require_cuda(func):
+    """
+    Decorator that skips the test if cuda is not available.
+    """
+    from functools import wraps
+
+    @wraps(func)
+    def wrapper(*args, **kwargs):
+        if not torch.cuda.is_available():
+            pytest.skip("requires cuda")
+        return func(*args, **kwargs)
+
+    return wrapper
+
+
 def require_env(func):
     """
     Decorator that skips the test if the required environment package is not installed.