test(rewards): add unit tests for distributional value function model

- Added a new distributional value function (DistributionalVF) model for RECAP, including its configuration, modeling, and processor components.
- Updated the rewards factory to support the new model type.
- Updated  to include the new model in the dependencies.

pyproject.toml

@@ -214,6 +214,7 @@ groot = [
 sarm = ["lerobot[transformers-dep]", "pydantic>=2.0.0,<3.0.0", "faker>=33.0.0,<35.0.0", "lerobot[matplotlib-dep]", "lerobot[qwen-vl-utils-dep]"]
 robometer = ["lerobot[transformers-dep]", "lerobot[qwen-vl-utils-dep]", "lerobot[peft-dep]"]
 topreward = ["lerobot[transformers-dep]"]
+recap = ["lerobot[transformers-dep]"]
 xvla = ["lerobot[transformers-dep]"]
 eo1 = ["lerobot[transformers-dep]", "lerobot[qwen-vl-utils-dep]"]
 hilserl = ["lerobot[transformers-dep]", "lerobot[dataset]", "gym-hil>=0.1.13,<0.2.0", "lerobot[grpcio-dep]", "lerobot[placo-dep]"]
@@ -296,6 +297,7 @@ all = [
     "lerobot[sarm]",
     "lerobot[robometer]",
     "lerobot[topreward]",
+    "lerobot[recap]",
     "lerobot[peft]",
     # "lerobot[unitree_g1]", TODO: Unitree requires specific installation instructions for unitree_sdk2
 ]

src/lerobot/rewards/__init__.py

@@ -13,6 +13,9 @@
 # limitations under the License.
 
 from .classifier.configuration_classifier import RewardClassifierConfig as RewardClassifierConfig
+from .distributional_value_function.configuration_distributional_value_function import (
+    DistributionalVFConfig as DistributionalVFConfig,
+)
 from .factory import (
     get_reward_model_class as get_reward_model_class,
     make_reward_model as make_reward_model,
@@ -26,6 +29,7 @@ from .topreward.configuration_topreward import TOPRewardConfig as TOPRewardConfi
 
 __all__ = [
     # Configuration classes
+    "DistributionalVFConfig",
     "RewardClassifierConfig",
     "RobometerConfig",
     "SARMConfig",

src/lerobot/rewards/distributional_value_function/__init__.py

@@ -0,0 +1,23 @@
+# Copyright 2025 The HuggingFace Inc. team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from .configuration_distributional_value_function import DistributionalVFConfig
+from .modeling_distributional_value_function import DistributionalVFRewardModel
+from .processor_distributional_value_function import make_distributional_vf_pre_post_processors
+
+__all__ = [
+    "DistributionalVFConfig",
+    "DistributionalVFRewardModel",
+    "make_distributional_vf_pre_post_processors",
+]

src/lerobot/rewards/distributional_value_function/configuration_distributional_value_function.py

@@ -0,0 +1,108 @@
+# Copyright 2025 The HuggingFace Inc. team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Configuration for RECAP's distributional value function.
+
+Paper: "π*0.6: a VLA That Learns From Experience" (Physical Intelligence, 2025)
+       https://pi.website/blog/pistar06
+
+Implements the distributional value function V^{pi_ref}(o_t, l) from Section IV-A.
+Architecture: the paper uses a 670M-parameter Gemma 3 VLM (the actor is 4B Gemma 3).
+We match that scale on PaliGemma (PI05's Gemma 2B backbone) by truncating to 6 Gemma
+LM layers and 13 SigLIP vision layers (~670M params), with a [CLS] token and linear
+head predicting a categorical distribution over B=201 discrete value bins in [-1, 0].
+
+Training: cross-entropy on HL-Gauss soft targets (or Dirac delta projection),
+with optional one-hot targets for terminal states; MC returns normalized per task.
+Weights initialized from a pre-trained PI05 actor checkpoint.
+"""
+
+from dataclasses import dataclass, field
+
+from lerobot.configs import FeatureType, NormalizationMode
+from lerobot.configs.rewards import RewardModelConfig
+from lerobot.optim import AdamWConfig, CosineDecayWithWarmupSchedulerConfig
+
+
+@RewardModelConfig.register_subclass("distributional_value_function")
+@dataclass
+class DistributionalVFConfig(RewardModelConfig):
+    """Configuration for RECAP's distributional value function.
+
+    The value function predicts V^{pi_ref}(o_t, l) as a distribution over B discrete
+    bins spanning [value_support_min, value_support_max]. It is trained with cross-entropy
+    on HL-Gauss soft targets or Dirac delta projection, derived from Monte Carlo returns
+    (Eq. 1 in the paper).
+
+    Architecture: the paper value function is a 670M Gemma 3 VLM; the actor is 4B Gemma 3.
+    We use truncated PaliGemma (``num_hidden_layers=6``, ``num_vision_layers=13``) to reach
+    about 670M params and initialize from the PI05 actor checkpoint.
+    """
+
+    # Backbone
+    paligemma_variant: str = "gemma_2b"
+    num_hidden_layers: int = 6
+    num_vision_layers: int = 13
+
+    # Distributional head
+    num_value_bins: int = 201
+    value_support_min: float = -1.0
+    value_support_max: float = 0.0
+    hl_gauss_sigma_ratio: float = 5.0
+
+    # Target distribution method: "hl_gauss" (default, soft) or "dirac_delta" (C51, hard)
+    target_method: str = "hl_gauss"
+
+    # Whether to use one-hot targets for terminal states (exact return, no smoothing).
+    # When False, terminal states use the same target method as non-terminal states.
+    use_one_hot_terminal: bool = True
+
+    # Image
+    image_resolution: tuple[int, int] = (224, 224)
+
+    # Tokenizer
+    tokenizer_max_length: int = 64
+
+    # Init from actor (required for first training: provides SigLIP vision tower + Gemma embeddings).
+    # Pass a PI05 checkpoint path or Hub repo_id here.
+    # After training, load the value function with RewardModel.from_pretrained() instead.
+    init_from_actor_path: str = ""
+
+    # Normalization
+    normalization_mapping: dict[str, NormalizationMode] = field(
+        default_factory=lambda: {
+            "VISUAL": NormalizationMode.IDENTITY,
+            "STATE": NormalizationMode.IDENTITY,
+        }
+    )
+
+    def get_optimizer_preset(self) -> AdamWConfig:
+        return AdamWConfig(
+            lr=3e-4,
+            weight_decay=1e-4,
+            grad_clip_norm=1.0,
+        )
+
+    def get_scheduler_preset(self) -> CosineDecayWithWarmupSchedulerConfig:
+        return CosineDecayWithWarmupSchedulerConfig(
+            num_warmup_steps=500,
+            num_decay_steps=50000,
+        )
+
+    def validate_features(self) -> None:
+        if not self.input_features:
+            return
+        has_image = any(ft.type == FeatureType.VISUAL for ft in self.input_features.values())
+        if not has_image:
+            raise ValueError("DistributionalVFConfig requires at least one VISUAL input feature.")

src/lerobot/rewards/distributional_value_function/modeling_distributional_value_function.py

@@ -0,0 +1,567 @@
+# Copyright 2025 The HuggingFace Inc. team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Modeling for RECAP's distributional value function.
+
+Paper: "π*0.6: a VLA That Learns From Experience" (Physical Intelligence, 2025)
+       https://pi.website/blog/pistar06
+
+Implements the distributional value function V^{pi_ref}(o_t, l) from Section IV-A.
+Architecture: the paper uses a 670M-parameter Gemma 3 VLM (the actor is 4B Gemma 3).
+We match that scale on PaliGemma (PI05's Gemma 2B backbone) by truncating to 6 Gemma
+LM layers and 13 SigLIP vision layers (~670M params), with a [CLS] token and linear
+head predicting a categorical distribution over B=201 discrete value bins in [-1, 0].
+
+Inputs: single image observation + task text prompt ("Task: {task}.")
+Outputs: softmax distribution over value bins; expected value E[V] for inference.
+Training: cross-entropy on HL-Gauss soft targets (or Dirac delta projection),
+with optional one-hot targets for terminal states; MC returns normalized per task.
+
+Weight initialization: vision tower, multi-modal projector, token embeddings, and
+the first N transformer layers are copied from a pre-trained PI05 actor checkpoint.
+"""
+
+from __future__ import annotations
+
+import math
+from typing import TYPE_CHECKING, Any
+
+import torch
+import torch.nn.functional as F  # noqa: N812
+from torch import Tensor, nn
+
+from lerobot.rewards.pretrained import PreTrainedRewardModel
+from lerobot.utils.import_utils import _transformers_available, require_package
+
+from .configuration_distributional_value_function import DistributionalVFConfig
+
+if TYPE_CHECKING or _transformers_available:
+    from transformers.models.auto import CONFIG_MAPPING
+    from transformers.models.gemma import modeling_gemma
+
+    from lerobot.policies.pi_gemma import (
+        PaliGemmaForConditionalGenerationWithPiGemma,
+        PiGemmaRMSNorm,
+        _gated_residual,
+        _get_pi_gemma_decoder_layer_base,
+    )
+else:
+    CONFIG_MAPPING = None
+    modeling_gemma = None
+    PaliGemmaForConditionalGenerationWithPiGemma = None
+    PiGemmaRMSNorm = None
+    _gated_residual = None
+    _get_pi_gemma_decoder_layer_base = None
+
+PALIGEMMA_VOCAB_SIZE = 257152
+
+
+class DistributionalVFRewardModel(PreTrainedRewardModel):
+    """Distributional value function model for RECAP.
+
+    Predicts V^{pi_ref}(o_t, l) as a categorical distribution over B bins (default 201).
+    Trained with cross-entropy on HL-Gauss or Dirac delta targets centered on
+    per-task normalized Monte Carlo returns.
+
+    Architecture: truncated PaliGemma (``num_hidden_layers=6``, ``num_vision_layers=13``),
+    causal attention, [CLS] token, and Linear(D, num_bins) value head.
+    The expected value is E[V] = sum(softmax(logits) * bin_centers).
+    """
+
+    name = "distributional_value_function"
+    config_class = DistributionalVFConfig
+
+    def __init__(self, config: DistributionalVFConfig, **kwargs) -> None:
+        require_package("transformers", extra="recap")
+        super().__init__(config)
+        self.config = config
+
+        from transformers.models.gemma.modeling_gemma import GemmaRotaryEmbedding
+
+        from lerobot.policies.pi05.modeling_pi05 import get_gemma_config
+
+        # Get base dimensions from the paligemma variant (OpenPI config format)
+        base_config = get_gemma_config(config.paligemma_variant)
+        hidden_dim = base_config.width
+        mlp_dim = base_config.mlp_dim
+        num_layers = config.num_hidden_layers
+
+        # HuggingFace GemmaConfig for transformer layers
+        gemma_config = CONFIG_MAPPING["gemma"](
+            head_dim=base_config.head_dim,
+            hidden_size=hidden_dim,
+            intermediate_size=mlp_dim,
+            num_attention_heads=base_config.num_heads,
+            num_hidden_layers=num_layers,
+            num_key_value_heads=base_config.num_kv_heads,
+            vocab_size=PALIGEMMA_VOCAB_SIZE,
+            hidden_activation="gelu_pytorch_tanh",
+        )
+        self.gemma_config = gemma_config
+        self.hidden_dim = hidden_dim
+        self.num_value_bins = config.num_value_bins
+
+        # Single learned [CLS] token for value prediction
+        self.cls_embedding = nn.Parameter(torch.randn(1, 1, hidden_dim) * 0.02)
+
+        # Value projection head: Linear(hidden_dim, num_bins)
+        self.value_head = nn.Linear(in_features=hidden_dim, out_features=config.num_value_bins)
+
+        # Transformer layers (overwritten by _initialize_from_actor on first run)
+        self.rotary_emb = GemmaRotaryEmbedding(gemma_config)
+        pi_gemma_decoder_layer_base = _get_pi_gemma_decoder_layer_base()
+        self.layers = nn.ModuleList(
+            [pi_gemma_decoder_layer_base(gemma_config, layer_idx=i) for i in range(num_layers)]
+        )
+        self.norm = PiGemmaRMSNorm(hidden_dim, eps=gemma_config.rms_norm_eps)
+
+        # Vision tower + projector + token embedding (overwritten by _initialize_from_actor on first run)
+        # PaliGemmaConfig wraps both vision and text configs into a single model
+        paligemma_config = CONFIG_MAPPING["paligemma"]()
+        paligemma_config.text_config = gemma_config
+        paligemma_config.vision_config.image_size = config.image_resolution[0]
+        paligemma_config.vision_config.intermediate_size = 4304
+        paligemma_config.vision_config.projection_dim = 2048
+        paligemma_config.vision_config.projector_hidden_act = "gelu_fast"
+
+        paligemma_full = PaliGemmaForConditionalGenerationWithPiGemma(config=paligemma_config)
+        self.vision_tower = paligemma_full.model.vision_tower
+        self.multi_modal_projector = paligemma_full.model.multi_modal_projector
+        self.token_embedding = paligemma_full.model.language_model.embed_tokens
+        del paligemma_full
+
+        # Truncate vision tower to num_vision_layers
+        if hasattr(self.vision_tower, "vision_model") and hasattr(self.vision_tower.vision_model, "encoder"):
+            vision_encoder = self.vision_tower.vision_model.encoder
+            vision_encoder.layers = vision_encoder.layers[: config.num_vision_layers]
+
+        # Bin support: evenly spaced centers from value_support_min to value_support_max
+        bin_centers = torch.linspace(config.value_support_min, config.value_support_max, self.num_value_bins)
+        self.register_buffer("bin_centers", bin_centers, persistent=False)
+        bin_width = (config.value_support_max - config.value_support_min) / (self.num_value_bins - 1)
+        self.hl_gauss_sigma = float(config.hl_gauss_sigma_ratio * bin_width)
+
+        # Overwrite with pre-trained PI05 actor weights (first training run only)
+        if config.init_from_actor_path:
+            self._initialize_from_actor()
+
+    def _initialize_from_actor(self) -> None:
+        """Overwrite weights from a pre-trained PI05 actor checkpoint.
+
+        Called on first training run only (when init_from_actor_path is set).
+        """
+        from lerobot.policies.pi05.modeling_pi05 import PI05Policy
+
+        actor_policy = PI05Policy.from_pretrained(self.config.init_from_actor_path)
+        actor_model = actor_policy.model
+
+        paligemma_model = actor_model.paligemma_with_expert.paligemma
+        source_language_model = paligemma_model.model.language_model
+
+        # Transformer components
+        self.rotary_emb.load_state_dict(source_language_model.rotary_emb.state_dict())
+        num_layers = self.gemma_config.num_hidden_layers
+        for i in range(num_layers):
+            self.layers[i].load_state_dict(source_language_model.layers[i].state_dict())
+        self.norm.load_state_dict(source_language_model.norm.state_dict())
+
+        # Vision tower (truncate source first, then copy)
+        source_vision_tower = paligemma_model.model.vision_tower
+        if hasattr(source_vision_tower, "vision_model") and hasattr(
+            source_vision_tower.vision_model, "encoder"
+        ):
+            source_encoder = source_vision_tower.vision_model.encoder
+            source_encoder.layers = source_encoder.layers[: self.config.num_vision_layers]
+        self.vision_tower.load_state_dict(source_vision_tower.state_dict())
+
+        # Multi-modal projector
+        self.multi_modal_projector.load_state_dict(paligemma_model.model.multi_modal_projector.state_dict())
+
+        # Token embedding table
+        self.token_embedding.load_state_dict(paligemma_model.model.language_model.embed_tokens.state_dict())
+
+        del actor_policy
+
+    def embed_image(self, image: Tensor) -> Tensor:
+        """Embed images using the value function's SigLIP vision tower.
+
+        Args:
+            image: [batch_size, channels, height, width] preprocessed images in [-1, 1].
+
+        Returns:
+            [batch_size, num_patches, hidden_dim] projected image features.
+        """
+        out_dtype = image.dtype
+        if image.dtype != torch.float32:
+            image = image.to(torch.float32)
+
+        image_outputs = self.vision_tower(image, return_dict=True)
+        image_features = self.multi_modal_projector(image_outputs.last_hidden_state)
+        image_features = image_features / (self.hidden_dim**0.5)
+
+        if image_features.dtype != out_dtype:
+            image_features = image_features.to(out_dtype)
+        return image_features
+
+    def embed_text(self, token_ids: Tensor) -> Tensor:
+        """Embed text token IDs using the value function's token embedding table.
+
+        Args:
+            token_ids: [batch_size, seq_len] integer token IDs
+
+        Returns:
+            [batch_size, seq_len, hidden_dim] text embeddings
+        """
+        return self.token_embedding(token_ids)
+
+    def _get_cls_embedding(self, batch_size: int) -> Tensor:
+        """Get [CLS] token embedding expanded to batch size.
+
+        Args:
+            batch_size: number of samples in the batch.
+
+        Returns:
+            [batch_size, 1, hidden_dim] learned [CLS] embedding.
+        """
+        return self.cls_embedding.expand(batch_size, -1, -1)
+
+    def forward_value(
+        self, vision_features: Tensor, text_embeddings: Tensor, text_padding_mask: Tensor
+    ) -> dict[str, Tensor]:
+        """Core forward pass through the distributional value function.
+
+        Args:
+            vision_features: [batch_size, num_patches, hidden_dim]
+            text_embeddings: [batch_size, seq_len, hidden_dim]
+            text_padding_mask: [batch_size, seq_len] boolean mask for text tokens
+
+        Returns:
+            logits: [batch_size, num_value_bins]
+            probs: [batch_size, num_value_bins]
+            value: [batch_size, 1]
+        """
+        from lerobot.utils.constants import OPENPI_ATTENTION_MASK_VALUE
+
+        batch_size = text_embeddings.shape[0]
+        device = text_embeddings.device
+
+        # Build sequence: [vision, text, CLS]
+        cls_embedding = self._get_cls_embedding(batch_size)
+        hidden_states = torch.cat([vision_features, text_embeddings, cls_embedding], dim=1)
+
+        # Build causal attention mask
+        vision_len = vision_features.shape[1]
+        vision_padding_mask = torch.ones(batch_size, vision_len, dtype=torch.bool, device=device)
+        cls_padding_mask = torch.ones(batch_size, 1, dtype=torch.bool, device=device)
+        full_padding_mask = torch.cat([vision_padding_mask, text_padding_mask, cls_padding_mask], dim=1)
+
+        full_seq_len = full_padding_mask.shape[1]
+
+        # Causal mask
+        causal_mask = torch.tril(torch.ones(full_seq_len, full_seq_len, device=device, dtype=torch.bool))
+        # Combine causal mask with padding mask
+        padding_mask_4d = full_padding_mask[:, None, None, :].expand(
+            batch_size, 1, full_seq_len, full_seq_len
+        )
+        attention_mask = causal_mask[None, None, :, :] & padding_mask_4d
+        attention_mask = torch.where(attention_mask, 0.0, OPENPI_ATTENTION_MASK_VALUE)
+
+        position_ids = torch.cumsum(full_padding_mask.long(), dim=1) - 1
+        cos, sin = self.rotary_emb(hidden_states, position_ids)
+
+        for layer in self.layers:
+            norm_output = layer.input_layernorm(hidden_states, cond=None)
+            if isinstance(norm_output, tuple):
+                hidden_states_normed, gate = norm_output
+            else:
+                hidden_states_normed, gate = norm_output, None
+
+            input_shape = hidden_states_normed.shape[:-1]
+            hidden_shape = (*input_shape, -1, layer.self_attn.head_dim)
+
+            query_states = layer.self_attn.q_proj(hidden_states_normed).view(hidden_shape).transpose(1, 2)
+            key_states = layer.self_attn.k_proj(hidden_states_normed).view(hidden_shape).transpose(1, 2)
+            value_states = layer.self_attn.v_proj(hidden_states_normed).view(hidden_shape).transpose(1, 2)
+
+            query_states, key_states = modeling_gemma.apply_rotary_pos_emb(
+                query_states, key_states, cos, sin, unsqueeze_dim=1
+            )
+
+            attention_output, _ = modeling_gemma.eager_attention_forward(
+                layer.self_attn,
+                query_states,
+                key_states,
+                value_states,
+                attention_mask,
+                layer.self_attn.scaling,
+            )
+
+            attention_output = attention_output.reshape(batch_size, -1, self.gemma_config.hidden_size)
+            if attention_output.dtype != layer.self_attn.o_proj.weight.dtype:
+                attention_output = attention_output.to(layer.self_attn.o_proj.weight.dtype)
+            projected_attention = layer.self_attn.o_proj(attention_output)
+
+            if gate is not None:
+                projected_attention = _gated_residual(hidden_states, projected_attention, gate)
+            else:
+                projected_attention = hidden_states + projected_attention
+
+            after_attention_residual = projected_attention.clone()
+
+            norm_output = layer.post_attention_layernorm(projected_attention, cond=None)
+            if isinstance(norm_output, tuple):
+                mlp_input, gate = norm_output
+            else:
+                mlp_input, gate = norm_output, None
+
+            mlp_output = layer.mlp(mlp_input)
+
+            if gate is not None:
+                hidden_states = _gated_residual(after_attention_residual, mlp_output, gate)
+            else:
+                hidden_states = after_attention_residual + mlp_output
+
+        hidden_states = self.norm(hidden_states)
+        if isinstance(hidden_states, tuple):
+            hidden_states = hidden_states[0]
+
+        # Extract [CLS] token (last position in the sequence)
+        cls_hidden_state = hidden_states[:, -1, :]  # [batch_size, hidden_dim]
+
+        # Value head: Linear(hidden_dim, num_bins) -> logits
+        value_logits = self.value_head(cls_hidden_state)  # [batch_size, num_value_bins]
+        value_probs = F.softmax(value_logits, dim=-1)
+        predicted_value = (value_probs * self.bin_centers.to(dtype=value_probs.dtype)).sum(
+            dim=-1, keepdim=True
+        )
+
+        return {"logits": value_logits, "probs": value_probs, "value": predicted_value}
+
+    def hl_gauss_target(self, target_value: Tensor) -> Tensor:
+        """HL-Gauss soft target distribution.
+
+        Places a Gaussian N(target, sigma^2) over the bin support and computes
+        per-bin probabilities as CDF differences at bin edges, normalized to sum to 1.
+
+        Reference: Farebrother et al. 2024, "Stop Regressing: Training Value
+        Functions via Classification for Scalable Deep RL", Section 3.1.
+        arXiv:2403.03950
+
+        Args:
+            target_value: [batch_size] or [batch_size, 1] target values.
+
+        Returns:
+            [batch_size, num_value_bins] target probability distribution.
+        """
+        if target_value.ndim == 2:
+            target_value = target_value.squeeze(-1)
+        target_value = target_value.to(dtype=self.bin_centers.dtype)
+
+        # Bin edges: half a bin-width outside the first/last center
+        bin_width = (self.config.value_support_max - self.config.value_support_min) / (
+            self.num_value_bins - 1
+        )
+        support_edges = torch.linspace(
+            self.config.value_support_min - bin_width / 2,
+            self.config.value_support_max + bin_width / 2,
+            self.num_value_bins + 1,
+            device=target_value.device,
+            dtype=target_value.dtype,
+        )
+
+        # CDF of N(target, sigma^2) evaluated at each edge
+        cdf_at_edges = 0.5 * (
+            1.0
+            + torch.erf(
+                (support_edges.unsqueeze(0) - target_value.unsqueeze(-1))
+                / (self.hl_gauss_sigma * math.sqrt(2))
+            )
+        )  # [batch_size, num_bins + 1]
+
+        # Normalize: z = cdf(max_edge) - cdf(min_edge)
+        normalization_constant = (cdf_at_edges[:, -1] - cdf_at_edges[:, 0]).unsqueeze(-1).clamp(min=1e-10)
+
+        # Bin probabilities = differences of consecutive CDF values, normalized
+        bin_probabilities = (cdf_at_edges[:, 1:] - cdf_at_edges[:, :-1]) / normalization_constant
+
+        return bin_probabilities
+
+    def dirac_delta_target(self, target_value: Tensor) -> Tensor:
+        """Dirac delta (C51) projection: split probability between two nearest bins.
+
+        Standard distributional RL projection from Bellemare et al. 2017.
+        "A Distributional Perspective on Reinforcement Learning"
+        arXiv:1707.06887
+
+        Args:
+            target_value: [batch_size] or [batch_size, 1] target values.
+
+        Returns:
+            [batch_size, num_value_bins] target probability distribution.
+        """
+        if target_value.ndim == 2:
+            target_value = target_value.squeeze(-1)
+        target_value = target_value.clamp(self.config.value_support_min, self.config.value_support_max)
+        target_value = target_value.to(dtype=self.bin_centers.dtype)
+
+        bin_width = self.bin_centers[1] - self.bin_centers[0]
+        normalized_position = (target_value - self.config.value_support_min) / bin_width
+        lower_bin_idx = normalized_position.floor().long().clamp(0, self.num_value_bins - 1)
+        upper_bin_idx = normalized_position.ceil().long().clamp(0, self.num_value_bins - 1)
+
+        weight_upper = normalized_position - lower_bin_idx.float()
+        weight_lower = upper_bin_idx.float() - normalized_position
+
+        same_bin = lower_bin_idx == upper_bin_idx
+        weight_upper = torch.where(same_bin, torch.zeros_like(weight_upper), weight_upper)
+        weight_lower = torch.where(same_bin, torch.ones_like(weight_lower), weight_lower)
+
+        batch_size = target_value.shape[0]
+        target_distribution = torch.zeros(batch_size, self.num_value_bins, device=target_value.device)
+        batch_indices = torch.arange(batch_size, device=target_value.device)
+        target_distribution[batch_indices, lower_bin_idx] += weight_lower
+        target_distribution[batch_indices, upper_bin_idx] += weight_upper
+
+        return target_distribution
+
+    def one_hot_target(self, target_value: Tensor) -> Tensor:
+        """One-hot target for terminal states (exact return, no smoothing).
+
+        Args:
+            target_value: [batch_size] or [batch_size, 1] target values.
+
+        Returns:
+            [batch_size, num_value_bins] one-hot distribution at the nearest bin.
+        """
+        if target_value.ndim == 2:
+            target_value = target_value.squeeze(-1)
+        target_value = target_value.to(dtype=self.bin_centers.dtype)
+        nearest_bin_idx = torch.argmin(
+            torch.abs(self.bin_centers.unsqueeze(0) - target_value.unsqueeze(-1)), dim=-1
+        )
+        return F.one_hot(nearest_bin_idx, num_classes=self.num_value_bins).to(dtype=self.bin_centers.dtype)
+
+    def compute_target_distribution(
+        self,
+        target_value: Tensor,
+        is_terminal: Tensor,
+        method: str = "hl_gauss",
+        use_one_hot_terminal: bool = True,
+    ) -> Tensor:
+        """Compute target distribution using configured method.
+
+        Args:
+            target_value: [batch_size] scalar return targets
+            is_terminal: [batch_size] boolean terminal flags
+            method: "hl_gauss" or "dirac_delta"
+            use_one_hot_terminal: if True, terminal states get one-hot targets
+                (exact return, no smoothing). If False, all states use the same method.
+
+        Returns:
+            [batch_size, num_value_bins] target probability distribution
+        """
+        if method == "hl_gauss":
+            base_distribution = self.hl_gauss_target(target_value)
+        elif method == "dirac_delta":
+            base_distribution = self.dirac_delta_target(target_value)
+        else:
+            raise ValueError(f"Unknown target method: {method}. Use 'hl_gauss' or 'dirac_delta'.")
+
+        if not use_one_hot_terminal:
+            return base_distribution
+
+        terminal_distribution = self.one_hot_target(target_value)
+
+        return torch.where(is_terminal[:, None].bool(), terminal_distribution, base_distribution)
+
+    def forward(self, batch: dict[str, Tensor]) -> tuple[Tensor, dict[str, Any]]:
+        """Training forward pass — computes cross-entropy loss against MC return targets.
+
+        The batch is expected to be preprocessed by the processor pipeline.
+        Keys expected in batch:
+            - observation.images.*: [B, C, H, W] preprocessed images
+            - observation.language_tokens: [B, seq_len] tokenized task prompt
+            - observation.language_attention_mask: [B, seq_len] padding mask
+            - mc_return: [B] normalized Monte Carlo return targets in (-1, 0)
+            - is_terminal: [B] boolean terminal flags
+
+        Returns:
+            (loss, output_dict) where loss is scalar cross-entropy
+        """
+        from lerobot.utils.constants import OBS_IMAGES, OBS_LANGUAGE_ATTENTION_MASK, OBS_LANGUAGE_TOKENS
+
+        # Get first image key from batch
+        image_keys = [k for k in batch if k.startswith(f"{OBS_IMAGES}.") or k == OBS_IMAGES]
+        if not image_keys:
+            raise KeyError(f"No image keys found in batch. Expected keys starting with '{OBS_IMAGES}.'")
+        images = batch[image_keys[0]]
+
+        token_ids = batch[OBS_LANGUAGE_TOKENS]
+        text_padding_mask = batch[OBS_LANGUAGE_ATTENTION_MASK].bool()
+        mc_return = batch["mc_return"]
+        is_terminal = batch["is_terminal"]
+
+        # Embed observations
+        vision_features = self.embed_image(images)
+        text_embeddings = self.embed_text(token_ids)
+
+        # Forward through value function transformer
+        vf_output = self.forward_value(vision_features, text_embeddings, text_padding_mask)
+        value_logits = vf_output["logits"]
+        predicted_value = vf_output["value"]
+
+        # Compute target distribution
+        target_distribution = self.compute_target_distribution(
+            mc_return,
+            is_terminal,
+            method=self.config.target_method,
+            use_one_hot_terminal=self.config.use_one_hot_terminal,
+        )
+
+        # Cross-entropy loss (Eq. 1 in pi*0.6 paper)
+        log_probs = F.log_softmax(value_logits, dim=-1)
+        loss = -(target_distribution * log_probs).sum(dim=-1).mean()
+
+        output_dict = {
+            "loss": loss.item(),
+            "predicted_value_mean": predicted_value.mean().item(),
+            "mc_return_mean": mc_return.mean().item(),
+        }
+
+        return loss, output_dict
+
+    def compute_reward(self, batch: dict[str, Tensor]) -> Tensor:
+        """Compute V(s) for a batch of observations. Used for advantage scoring.
+
+        Args:
+            batch: preprocessed batch with images and tokenized text
+
+        Returns:
+            [batch_size] tensor of predicted values V(s)
+        """
+        from lerobot.utils.constants import OBS_IMAGES, OBS_LANGUAGE_ATTENTION_MASK, OBS_LANGUAGE_TOKENS
+
+        image_keys = [k for k in batch if k.startswith(f"{OBS_IMAGES}.") or k == OBS_IMAGES]
+        if not image_keys:
+            raise KeyError(f"No image keys found in batch. Expected keys starting with '{OBS_IMAGES}.'")
+        images = batch[image_keys[0]]
+
+        token_ids = batch[OBS_LANGUAGE_TOKENS]
+        text_padding_mask = batch[OBS_LANGUAGE_ATTENTION_MASK].bool()
+
+        vision_features = self.embed_image(images)
+        text_embeddings = self.embed_text(token_ids)
+
+        vf_output = self.forward_value(vision_features, text_embeddings, text_padding_mask)
+        return vf_output["value"].squeeze(-1)  # [batch_size]

src/lerobot/rewards/distributional_value_function/processor_distributional_value_function.py

@@ -0,0 +1,235 @@
+# Copyright 2025 The HuggingFace Inc. team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Processor for RECAP's distributional value function.
+
+Paper: "π*0.6: a VLA That Learns From Experience" (Physical Intelligence, 2025)
+       https://pi.website/blog/pistar06
+
+Prepares inputs for V^{pi_ref}(o_t, l): single image observation and task text only.
+1. Image preprocessing (resize-with-pad + normalize to [-1, 1]) for SigLIP
+2. Task prompt formatting ("Task: {task}.") and tokenization via PaliGemma tokenizer
+
+Training targets (mc_return, is_terminal) are NOT routed through the processor.
+They are dataset columns read directly from the batch in the model's forward().
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import Any
+
+import torch
+from torch import Tensor
+
+from lerobot.configs import FeatureType, PipelineFeatureType, PolicyFeature
+from lerobot.processor import (
+    AddBatchDimensionProcessorStep,
+    DeviceProcessorStep,
+    NormalizerProcessorStep,
+    PolicyAction,
+    PolicyProcessorPipeline,
+    ProcessorStep,
+    ProcessorStepRegistry,
+    RenameObservationsProcessorStep,
+    TokenizerProcessorStep,
+    batch_to_transition,
+    policy_action_to_transition,
+    transition_to_batch,
+)
+from lerobot.processor.converters import to_tensor
+from lerobot.types import EnvTransition, TransitionKey
+from lerobot.utils.constants import (
+    OBS_IMAGES,
+    POLICY_POSTPROCESSOR_DEFAULT_NAME,
+    POLICY_PREPROCESSOR_DEFAULT_NAME,
+)
+
+from .configuration_distributional_value_function import DistributionalVFConfig
+
+PALIGEMMA_TOKENIZER_NAME = "google/paligemma-3b-pt-224"
+
+
+@ProcessorStepRegistry.register(name="distributional_vf_prepare_task_prompt")
+@dataclass
+class DistributionalVFPrepareTaskPromptStep(ProcessorStep):
+    """Format the task string for the distributional value function.
+
+    The value function receives only visual observations and task text.
+    Builds prompt: "Task: {task}."
+    """
+
+    task_key: str = "task"
+
+    def __call__(self, transition: EnvTransition) -> EnvTransition:
+        transition = transition.copy()
+
+        complementary_data = transition.get(TransitionKey.COMPLEMENTARY_DATA, {})
+        tasks = complementary_data.get(self.task_key)
+        if tasks is None:
+            raise ValueError("No task found in complementary data")
+
+        if isinstance(tasks, str):
+            tasks = [tasks]
+
+        full_prompts = []
+        for task in tasks:
+            cleaned_text = task.strip().replace("_", " ").replace("\n", " ")
+            full_prompts.append(f"Task: {cleaned_text}.")
+
+        new_complementary_data = dict(complementary_data)
+        new_complementary_data[self.task_key] = full_prompts
+        transition[TransitionKey.COMPLEMENTARY_DATA] = new_complementary_data
+        return transition
+
+    def transform_features(
+        self, features: dict[PipelineFeatureType, dict[str, PolicyFeature]]
+    ) -> dict[PipelineFeatureType, dict[str, PolicyFeature]]:
+        return features
+
+    def get_config(self) -> dict[str, Any]:
+        return {"task_key": self.task_key}
+
+
+@ProcessorStepRegistry.register(name="distributional_vf_image_preprocessor")
+@dataclass
+class DistributionalVFImagePreprocessorStep(ProcessorStep):
+    """Resize and normalize images for the value function's SigLIP vision tower.
+
+    Expects float images in [0, 1].
+    - Resize-with-pad to ``image_resolution`` (preserves aspect ratio)
+    - Scale to [-1, 1] for SigLIP
+    """
+
+    image_resolution: tuple[int, int] = (224, 224)
+    image_keys: tuple[str, ...] | None = None
+
+    def __call__(self, transition: EnvTransition) -> EnvTransition:
+        from lerobot.policies.pi05.modeling_pi05 import resize_with_pad_torch
+
+        observation = transition.get(TransitionKey.OBSERVATION)
+        if not isinstance(observation, dict):
+            raise ValueError("DistributionalVFImagePreprocessorStep requires an observation dict")
+
+        image_keys = self.image_keys or tuple(
+            key for key in observation if key == OBS_IMAGES or key.startswith(f"{OBS_IMAGES}.")
+        )
+        if not image_keys:
+            raise KeyError(
+                f"Distributional value function expected image keys under {OBS_IMAGES!r} in observation"
+            )
+
+        new_observation = dict(observation)
+        for image_key in image_keys:
+            image = new_observation[image_key]
+            if not isinstance(image, Tensor):
+                image = to_tensor(image)
+            if image.dtype != torch.float32:
+                image = image.to(torch.float32)
+
+            is_channels_first = image.ndim == 4 and image.shape[1] == 3
+            if is_channels_first:
+                image = image.permute(0, 2, 3, 1)
+
+            if image.shape[1:3] != self.image_resolution:
+                image = resize_with_pad_torch(image, *self.image_resolution)
+
+            image = image * 2.0 - 1.0
+
+            if is_channels_first:
+                image = image.permute(0, 3, 1, 2)
+
+            new_observation[image_key] = image
+
+        new_transition = transition.copy()
+        new_transition[TransitionKey.OBSERVATION] = new_observation
+        return new_transition
+
+    def transform_features(
+        self, features: dict[PipelineFeatureType, dict[str, PolicyFeature]]
+    ) -> dict[PipelineFeatureType, dict[str, PolicyFeature]]:
+        return features
+
+    def get_config(self) -> dict[str, Any]:
+        return {
+            "image_resolution": self.image_resolution,
+            "image_keys": list(self.image_keys) if self.image_keys is not None else None,
+        }
+
+
+def _visual_image_keys(config: DistributionalVFConfig) -> tuple[str, ...]:
+    return tuple(
+        feature_name
+        for feature_name, feature in config.input_features.items()
+        if feature.type == FeatureType.VISUAL
+    )
+
+
+def make_distributional_vf_pre_post_processors(
+    config: DistributionalVFConfig,
+    dataset_stats: dict[str, dict[str, torch.Tensor]] | None = None,
+) -> tuple[
+    PolicyProcessorPipeline[dict[str, Any], dict[str, Any]],
+    PolicyProcessorPipeline[PolicyAction, PolicyAction],
+]:
+    """Create pre/post processors for the distributional value function.
+
+    Preprocessor steps:
+        1. Rename observations (no-op by default)
+        2. Add a batch dimension
+        3. Normalize features (images use identity, so they stay in [0, 1])
+        4. Format task prompt: "Task: {task}."
+        5. Tokenize with the PaliGemma tokenizer
+        6. Resize-with-pad and scale images to [-1, 1] for SigLIP
+        7. Move tensors to the configured device
+
+    Training targets (mc_return, is_terminal) are not processed here.
+    The model reads them directly from the batch in forward().
+
+    The postprocessor is a no-op because the value function does not need
+    action postprocessing.
+    """
+    image_keys = _visual_image_keys(config)
+
+    preprocessor = PolicyProcessorPipeline[dict[str, Any], dict[str, Any]](
+        steps=[
+            RenameObservationsProcessorStep(rename_map={}),
+            AddBatchDimensionProcessorStep(),
+            NormalizerProcessorStep(
+                features={**config.input_features, **config.output_features},
+                norm_map=config.normalization_mapping,
+                stats=dataset_stats,
+            ),
+            DistributionalVFPrepareTaskPromptStep(),
+            TokenizerProcessorStep(
+                tokenizer_name=PALIGEMMA_TOKENIZER_NAME,
+                max_length=config.tokenizer_max_length,
+                padding_side="right",
+                padding="max_length",
+            ),
+            DistributionalVFImagePreprocessorStep(
+                image_resolution=config.image_resolution,
+                image_keys=image_keys or None,
+            ),
+            DeviceProcessorStep(device=config.device or "cpu"),
+        ],
+        name=POLICY_PREPROCESSOR_DEFAULT_NAME,
+        to_transition=batch_to_transition,
+        to_output=transition_to_batch,
+    )
+    postprocessor = PolicyProcessorPipeline(
+        name=POLICY_POSTPROCESSOR_DEFAULT_NAME,
+        to_transition=policy_action_to_transition,
+    )
+    return preprocessor, postprocessor

src/lerobot/rewards/factory.py

@@ -24,6 +24,7 @@ from lerobot.configs.rewards import RewardModelConfig
 from lerobot.processor import PolicyAction, PolicyProcessorPipeline
 
 from .classifier.configuration_classifier import RewardClassifierConfig
+from .distributional_value_function.configuration_distributional_value_function import DistributionalVFConfig
 from .pretrained import PreTrainedRewardModel
 from .robometer.configuration_robometer import RobometerConfig
 from .sarm.configuration_sarm import SARMConfig
@@ -63,6 +64,12 @@ def get_reward_model_class(name: str) -> type[PreTrainedRewardModel]:
         from lerobot.rewards.topreward.modeling_topreward import TOPRewardModel
 
         return TOPRewardModel
+    elif name == "distributional_value_function":
+        from lerobot.rewards.distributional_value_function.modeling_distributional_value_function import (
+            DistributionalVFRewardModel,
+        )
+
+        return DistributionalVFRewardModel
     else:
         try:
             return _get_reward_model_cls_from_name(name=name)
@@ -96,6 +103,8 @@ def make_reward_model_config(reward_type: str, **kwargs) -> RewardModelConfig:
         return RobometerConfig(**kwargs)
     elif reward_type == "topreward":
         return TOPRewardConfig(**kwargs)
+    elif reward_type == "distributional_value_function":
+        return DistributionalVFConfig(**kwargs)
     else:
         try:
             config_cls = RewardModelConfig.get_choice_class(reward_type)
@@ -191,6 +200,16 @@ def make_reward_pre_post_processors(
             dataset_stats=kwargs.get("dataset_stats"),
         )
 
+    elif isinstance(reward_cfg, DistributionalVFConfig):
+        from lerobot.rewards.distributional_value_function.processor_distributional_value_function import (
+            make_distributional_vf_pre_post_processors,
+        )
+
+        return make_distributional_vf_pre_post_processors(
+            config=reward_cfg,
+            dataset_stats=kwargs.get("dataset_stats"),
+        )
+
     else:
         try:
             processors = _make_processors_from_reward_model_config(

tests/rewards/test_distributional_value_function.py

@@ -0,0 +1,518 @@
+# Copyright 2025 The HuggingFace Inc. team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Tests for RECAP's distributional value function."""
+
+from __future__ import annotations
+
+import pytest
+import torch
+
+from lerobot.configs.rewards import RewardModelConfig
+from lerobot.configs.types import FeatureType, NormalizationMode, PolicyFeature
+from lerobot.rewards.distributional_value_function.configuration_distributional_value_function import (
+    DistributionalVFConfig,
+)
+from lerobot.types import TransitionKey
+from lerobot.utils.constants import OBS_IMAGES
+from tests.utils import skip_if_package_missing
+
+BATCH_SIZE = 4
+NUM_BINS = 201
+IMAGE_KEY = f"{OBS_IMAGES}.top"
+
+
+def _make_config(**overrides) -> DistributionalVFConfig:
+    defaults = {
+        "init_from_actor_path": "",
+        "device": "cpu",
+        "image_resolution": (224, 224),
+    }
+    defaults.update(overrides)
+    config = DistributionalVFConfig(**defaults)
+    config.input_features = {
+        IMAGE_KEY: PolicyFeature(type=FeatureType.VISUAL, shape=(3, 224, 224)),
+    }
+    config.output_features = {}
+    config.normalization_mapping = {
+        "VISUAL": NormalizationMode.IDENTITY,
+    }
+    return config
+
+
+def _make_model():
+    from lerobot.rewards.distributional_value_function.modeling_distributional_value_function import (
+        DistributionalVFRewardModel,
+    )
+
+    return DistributionalVFRewardModel(_make_config())
+
+
+def _make_batch(batch_size: int = BATCH_SIZE, device: str = "cpu") -> dict[str, torch.Tensor]:
+    from lerobot.utils.constants import OBS_LANGUAGE_ATTENTION_MASK, OBS_LANGUAGE_TOKENS
+
+    return {
+        IMAGE_KEY: torch.rand(batch_size, 3, 224, 224, device=device),
+        OBS_LANGUAGE_TOKENS: torch.randint(0, 1000, (batch_size, 16), device=device),
+        OBS_LANGUAGE_ATTENTION_MASK: torch.ones(batch_size, 16, dtype=torch.bool, device=device),
+        "mc_return": torch.rand(batch_size, device=device) * -1.0,
+        "is_terminal": torch.zeros(batch_size, dtype=torch.bool, device=device),
+    }
+
+
+def test_config_registered_in_reward_model_registry():
+    """DistributionalVFConfig is discoverable via RewardModelConfig registry."""
+    known = RewardModelConfig.get_known_choices()
+    assert "distributional_value_function" in known
+
+
+def test_factory_returns_correct_class():
+    """get_reward_model_class returns DistributionalVFRewardModel."""
+    from lerobot.rewards.factory import get_reward_model_class
+
+    cls = get_reward_model_class("distributional_value_function")
+    from lerobot.rewards.distributional_value_function.modeling_distributional_value_function import (
+        DistributionalVFRewardModel,
+    )
+
+    assert cls is DistributionalVFRewardModel
+
+
+def test_make_reward_model_config_factory():
+    """make_reward_model_config creates DistributionalVFConfig with overrides."""
+    from lerobot.rewards.factory import make_reward_model_config
+
+    config = make_reward_model_config("distributional_value_function", num_value_bins=101)
+    assert isinstance(config, DistributionalVFConfig)
+    assert config.num_value_bins == 101
+
+
+@skip_if_package_missing("transformers")
+def test_hl_gauss_sums_to_one():
+    """HL-Gauss target distribution sums to 1 for each sample."""
+    model = _make_model()
+    targets = torch.tensor([-0.5, -0.1, -0.9, -0.0])
+    dist = model.hl_gauss_target(targets)
+
+    assert dist.shape == (4, NUM_BINS)
+    torch.testing.assert_close(dist.sum(dim=-1), torch.ones(4), atol=1e-5, rtol=0)
+
+
+@skip_if_package_missing("transformers")
+def test_hl_gauss_non_negative():
+    """HL-Gauss target probabilities are all non-negative."""
+    model = _make_model()
+    targets = torch.linspace(-1.0, 0.0, 10)
+    dist = model.hl_gauss_target(targets)
+
+    assert (dist >= 0).all()
+
+
+@skip_if_package_missing("transformers")
+def test_hl_gauss_expected_value_matches():
+    """E[V] under HL-Gauss distribution matches the target value."""
+    model = _make_model()
+    targets = torch.tensor([-0.5, -0.1, -0.9])
+    dist = model.hl_gauss_target(targets)
+    expected = (dist * model.bin_centers).sum(dim=-1)
+
+    torch.testing.assert_close(expected, targets, atol=1e-4, rtol=0)
+
+
+@skip_if_package_missing("transformers")
+def test_hl_gauss_handles_2d_input():
+    """HL-Gauss handles [batch_size, 1] shaped inputs correctly."""
+    model = _make_model()
+    targets = torch.tensor([-0.5, -0.3]).unsqueeze(-1)
+    dist = model.hl_gauss_target(targets)
+
+    assert dist.shape == (2, NUM_BINS)
+    torch.testing.assert_close(dist.sum(dim=-1), torch.ones(2), atol=1e-5, rtol=0)
+
+
+@skip_if_package_missing("transformers")
+def test_dirac_delta_sums_to_one():
+    """Dirac delta target distribution sums to 1 for each sample."""
+    model = _make_model()
+    targets = torch.tensor([-0.5, -0.1, -0.9, -1.0, 0.0])
+    dist = model.dirac_delta_target(targets)
+
+    assert dist.shape == (5, NUM_BINS)
+    torch.testing.assert_close(dist.sum(dim=-1), torch.ones(5), atol=1e-6, rtol=0)
+
+
+@skip_if_package_missing("transformers")
+def test_dirac_delta_at_most_two_nonzero():
+    """Dirac delta places probability on at most two adjacent bins."""
+    model = _make_model()
+    targets = torch.tensor([-0.7523, -0.0013])
+    dist = model.dirac_delta_target(targets)
+
+    for i in range(2):
+        assert (dist[i] > 0).sum() <= 2
+
+
+@skip_if_package_missing("transformers")
+def test_dirac_delta_expected_value_matches():
+    """E[V] under Dirac delta distribution matches the target value."""
+    model = _make_model()
+    targets = torch.tensor([-0.5, -0.1, -0.9])
+    dist = model.dirac_delta_target(targets)
+    expected = (dist * model.bin_centers).sum(dim=-1)
+
+    torch.testing.assert_close(expected, targets, atol=1e-5, rtol=0)
+
+
+@skip_if_package_missing("transformers")
+def test_dirac_delta_boundary_values_clamped():
+    """Values outside support are clamped to boundary bins."""
+    model = _make_model()
+    targets = torch.tensor([-1.5, 0.5])
+    dist = model.dirac_delta_target(targets)
+
+    torch.testing.assert_close(dist.sum(dim=-1), torch.ones(2), atol=1e-6, rtol=0)
+    assert dist[0, 0] == 1.0
+    assert dist[1, -1] == 1.0
+
+
+@skip_if_package_missing("transformers")
+def test_one_hot_single_nonzero():
+    """One-hot target has exactly one non-zero bin per sample."""
+    model = _make_model()
+    targets = torch.tensor([-0.5, -0.1, -1.0, 0.0])
+    dist = model.one_hot_target(targets)
+
+    assert dist.shape == (4, NUM_BINS)
+    for i in range(4):
+        assert (dist[i] > 0).sum() == 1
+        assert dist[i].sum() == 1.0
+
+
+@skip_if_package_missing("transformers")
+def test_one_hot_nearest_bin():
+    """One-hot target activates the bin closest to the target value."""
+    model = _make_model()
+    targets = torch.tensor([-0.5])
+    dist = model.one_hot_target(targets)
+
+    hot_idx = dist[0].argmax()
+    assert model.bin_centers[hot_idx].item() == pytest.approx(-0.5, abs=0.003)
+
+
+@skip_if_package_missing("transformers")
+def test_terminal_gets_one_hot():
+    """Terminal states receive one-hot targets; non-terminal get HL-Gauss."""
+    model = _make_model()
+    targets = torch.tensor([-0.5, -0.3, -0.7, -0.9])
+    is_terminal = torch.tensor([False, True, False, True])
+
+    dist = model.compute_target_distribution(
+        targets, is_terminal, method="hl_gauss", use_one_hot_terminal=True
+    )
+
+    for i in range(4):
+        assert dist[i].sum().item() == pytest.approx(1.0, abs=1e-5)
+    assert (dist[1] > 0).sum() == 1
+    assert (dist[3] > 0).sum() == 1
+    assert (dist[0] > 0).sum() > 2
+    assert (dist[2] > 0).sum() > 2
+
+
+@skip_if_package_missing("transformers")
+def test_no_terminal_override_when_disabled():
+    """When use_one_hot_terminal=False, terminal states use the base method."""
+    model = _make_model()
+    targets = torch.tensor([-0.5, -0.3])
+    is_terminal = torch.tensor([False, True])
+
+    dist = model.compute_target_distribution(
+        targets, is_terminal, method="hl_gauss", use_one_hot_terminal=False
+    )
+
+    assert (dist[1] > 0).sum() > 2
+
+
+@skip_if_package_missing("transformers")
+def test_model_has_expected_components():
+    """Model scaffold contains all architectural components."""
+    model = _make_model()
+
+    assert hasattr(model, "vision_tower")
+    assert hasattr(model, "multi_modal_projector")
+    assert hasattr(model, "token_embedding")
+    assert hasattr(model, "layers")
+    assert hasattr(model, "value_head")
+    assert hasattr(model, "cls_embedding")
+    assert hasattr(model, "norm")
+    assert hasattr(model, "rotary_emb")
+    assert hasattr(model, "bin_centers")
+
+
+@skip_if_package_missing("transformers")
+def test_model_bin_centers_shape():
+    """Bin centers buffer has shape (num_value_bins,)."""
+    model = _make_model()
+    assert model.bin_centers.shape == (NUM_BINS,)
+
+
+@skip_if_package_missing("transformers")
+def test_model_layer_count():
+    """Transformer has num_hidden_layers (6) layers."""
+    model = _make_model()
+    assert len(model.layers) == 6
+
+
+@skip_if_package_missing("transformers")
+def test_model_value_head_output_dim():
+    """Value head outputs num_value_bins logits."""
+    model = _make_model()
+    assert model.value_head.out_features == NUM_BINS
+
+
+@skip_if_package_missing("transformers")
+def test_forward_returns_loss_and_dict():
+    """Forward pass returns a finite scalar loss and output dict with expected keys."""
+    model = _make_model()
+    batch = _make_batch()
+
+    loss, output_dict = model.forward(batch)
+
+    assert loss.shape == ()
+    assert torch.isfinite(loss)
+    assert "loss" in output_dict
+    assert "predicted_value_mean" in output_dict
+    assert "mc_return_mean" in output_dict
+
+
+@skip_if_package_missing("transformers")
+def test_forward_loss_is_positive():
+    """Cross-entropy loss is strictly positive for random weights."""
+    model = _make_model()
+    batch = _make_batch()
+
+    loss, _ = model.forward(batch)
+
+    assert loss.item() > 0
+
+
+@skip_if_package_missing("transformers")
+def test_compute_reward_returns_correct_shape():
+    """compute_reward returns [batch_size] tensor of finite float32 values."""
+    model = _make_model()
+    model.eval()
+    batch = _make_batch(batch_size=3)
+
+    with torch.no_grad():
+        values = model.compute_reward(batch)
+
+    assert values.shape == (3,)
+    assert values.dtype == torch.float32
+    assert torch.isfinite(values).all()
+
+
+@skip_if_package_missing("transformers")
+def test_compute_reward_values_in_support_range():
+    """Predicted values lie within [value_support_min, value_support_max]."""
+    model = _make_model()
+    model.eval()
+    batch = _make_batch(batch_size=8)
+
+    with torch.no_grad():
+        values = model.compute_reward(batch)
+
+    assert (values >= -1.0 - 0.01).all()
+    assert (values <= 0.0 + 0.01).all()
+
+
+@skip_if_package_missing("transformers")
+def test_processor_pipeline_produces_expected_keys():
+    """Full preprocessor pipeline produces tokenized text and processed images."""
+    from lerobot.rewards.distributional_value_function.processor_distributional_value_function import (
+        make_distributional_vf_pre_post_processors,
+    )
+    from lerobot.utils.constants import OBS_LANGUAGE_ATTENTION_MASK, OBS_LANGUAGE_TOKENS
+
+    config = _make_config()
+    preprocessor, _ = make_distributional_vf_pre_post_processors(config)
+
+    raw_batch = {
+        IMAGE_KEY: torch.rand(3, 224, 224),
+        "task": "pick up the cup",
+    }
+
+    processed = preprocessor(raw_batch)
+
+    assert OBS_LANGUAGE_TOKENS in processed
+    assert OBS_LANGUAGE_ATTENTION_MASK in processed
+    assert IMAGE_KEY in processed
+
+
+@skip_if_package_missing("transformers")
+def test_gradient_flows_through_value_head():
+    """Backprop produces non-zero gradients on the value head."""
+    model = _make_model()
+    model.train()
+    batch = _make_batch()
+
+    loss, _ = model.forward(batch)
+    loss.backward()
+
+    assert model.value_head.weight.grad is not None
+    assert not torch.all(model.value_head.weight.grad == 0)
+
+
+@skip_if_package_missing("transformers")
+def test_gradient_flows_through_cls_embedding():
+    """Backprop produces non-zero gradients on the learned [CLS] embedding."""
+    model = _make_model()
+    model.train()
+    batch = _make_batch()
+
+    loss, _ = model.forward(batch)
+    loss.backward()
+
+    assert model.cls_embedding.grad is not None
+    assert not torch.all(model.cls_embedding.grad == 0)
+
+
+def test_config_requires_visual_feature():
+    """validate_features raises if no VISUAL feature is present."""
+    config = DistributionalVFConfig(init_from_actor_path="")
+    config.input_features = {
+        "observation.state": PolicyFeature(type=FeatureType.STATE, shape=(14,)),
+    }
+
+    with pytest.raises(ValueError, match="VISUAL"):
+        config.validate_features()
+
+
+def test_config_passes_with_visual_feature():
+    """validate_features succeeds when a VISUAL feature is present."""
+    config = _make_config()
+    config.validate_features()
+
+
+@skip_if_package_missing("transformers")
+def test_save_load_pretrained_roundtrip(tmp_path):
+    """Saved model can be loaded back with identical weights."""
+    from lerobot.rewards.distributional_value_function.modeling_distributional_value_function import (
+        DistributionalVFRewardModel,
+    )
+
+    model = _make_model()
+    model._save_pretrained(tmp_path)
+
+    loaded = DistributionalVFRewardModel.from_pretrained(str(tmp_path))
+
+    orig_sd = model.state_dict()
+    loaded_sd = loaded.state_dict()
+
+    assert set(orig_sd.keys()) == set(loaded_sd.keys())
+    for key in orig_sd:
+        torch.testing.assert_close(orig_sd[key], loaded_sd[key], msg=f"Mismatch in {key}")
+
+
+@skip_if_package_missing("transformers")
+def test_image_preprocessor_normalizes_to_minus_one_one():
+    """Image preprocessor scales [0, 1] float input to [-1, 1] for SigLIP."""
+    from lerobot.rewards.distributional_value_function.processor_distributional_value_function import (
+        DistributionalVFImagePreprocessorStep,
+    )
+
+    step = DistributionalVFImagePreprocessorStep(image_resolution=(224, 224), image_keys=(IMAGE_KEY,))
+
+    transition = {
+        TransitionKey.OBSERVATION: {
+            IMAGE_KEY: torch.rand(1, 224, 224, 3),
+        },
+    }
+
+    result = step(transition)
+    image = result[TransitionKey.OBSERVATION][IMAGE_KEY]
+
+    assert image.min() >= -1.0 - 1e-5
+    assert image.max() <= 1.0 + 1e-5
+
+
+@skip_if_package_missing("transformers")
+def test_image_preprocessor_resizes_with_pad():
+    """Image preprocessor resizes non-square images to target resolution."""
+    from lerobot.rewards.distributional_value_function.processor_distributional_value_function import (
+        DistributionalVFImagePreprocessorStep,
+    )
+
+    step = DistributionalVFImagePreprocessorStep(image_resolution=(224, 224), image_keys=(IMAGE_KEY,))
+
+    transition = {
+        TransitionKey.OBSERVATION: {
+            IMAGE_KEY: torch.rand(1, 480, 640, 3),
+        },
+    }
+
+    result = step(transition)
+    image = result[TransitionKey.OBSERVATION][IMAGE_KEY]
+
+    assert image.shape[1:3] == (224, 224)
+
+
+def test_task_prompt_formats_correctly():
+    """Task prompt step converts underscored task to 'Task: {text}.' format."""
+    from lerobot.rewards.distributional_value_function.processor_distributional_value_function import (
+        DistributionalVFPrepareTaskPromptStep,
+    )
+
+    step = DistributionalVFPrepareTaskPromptStep()
+
+    transition = {
+        TransitionKey.COMPLEMENTARY_DATA: {"task": ["pick_up_the_cup"]},
+    }
+
+    result = step(transition)
+    prompt = result[TransitionKey.COMPLEMENTARY_DATA]["task"][0]
+
+    assert prompt == "Task: pick up the cup."
+
+
+def test_task_prompt_handles_string_input():
+    """Task prompt step accepts a plain string (not just a list)."""
+    from lerobot.rewards.distributional_value_function.processor_distributional_value_function import (
+        DistributionalVFPrepareTaskPromptStep,
+    )
+
+    step = DistributionalVFPrepareTaskPromptStep()
+
+    transition = {
+        TransitionKey.COMPLEMENTARY_DATA: {"task": "open_drawer"},
+    }
+
+    result = step(transition)
+    prompt = result[TransitionKey.COMPLEMENTARY_DATA]["task"][0]
+
+    assert prompt == "Task: open drawer."
+
+
+def test_task_prompt_raises_on_missing_task():
+    """Task prompt step raises ValueError when task key is absent."""
+    from lerobot.rewards.distributional_value_function.processor_distributional_value_function import (
+        DistributionalVFPrepareTaskPromptStep,
+    )
+
+    step = DistributionalVFPrepareTaskPromptStep()
+
+    transition = {
+        TransitionKey.COMPLEMENTARY_DATA: {},
+    }
+
+    with pytest.raises(ValueError, match="No task found"):
+        step(transition)