Diffusion Policies in Offline Reinforcement Learning (Diffusion-QL)

Diffusion policies are a class of highly expressive, sample-based policies for sequential decision-making, in which actions are generated via a learned reverse diffusion process, typically conditioned on environment context such as the current state or observation. They leverage denoising diffusion models—originally advanced in generative modeling—enabling the policy to match arbitrarily complex, multi-modal action distributions in both imitation and reinforcement learning frameworks. The principle advantage of diffusion policies lies in their ability to accurately model and regularize behaviors seen in diverse and multi-strategy offline datasets, which is critical for robust policy improvement in challenging real-world tasks.

1. Expressiveness of Diffusion Policies in Offline RL

Diffusion policies address the expressiveness bottleneck encountered by previous offline RL policy classes such as unimodal Gaussians or variational autoencoders (VAEs). In standard offline RL, models are trained entirely from a static dataset $\mathcal{B}$, usually collected from a behavior policy $\pi_b$, which may be complex and highly multi-modal (e.g., diverse human demonstrators or multiple strategies). Limited policy classes can only regularize toward or explore within a restricted policy family, resulting in suboptimal solutions due to distribution shift and function approximation errors.

Diffusion models, by contrast, learn the conditional distribution over actions via a learned denoising trajectory: $$\pi_\theta(a \mid s) = p_\theta(a^{0:N} \mid s) = \mathcal{N}(a^N; \mathbf{0}, I) \prod_{i=1}^N p_\theta(a^{i-1} \mid a^i, s)$$ Here, $a^0$ is the sampled action, and the reverse chain is parameterized to decode noise into meaningful action via a neural network, effectively allowing the policy to represent the full support (and multi-modality) of the dataset distribution.

Crucially, this expressiveness is not just a theoretical property: experiments confirm that decoders based on diffusion policies can resolve multiple, separated modes in synthetic and real datasets, outperforming Gaussian or mixture models which tend to average out or miss modes entirely.

2. The Diffusion Q-Learning (Diffusion-QL) Framework

Diffusion-QL articulates diffusion policies within an offline RL setting by coupling two objectives into a single training loss: $$\mathcal{L}(\theta) = \mathcal{L}_d(\theta) - \alpha \cdot \mathbb{E}_{s, a^0}[Q_\phi(s, a^0)]$$

• $\mathcal{L}_d(\theta)$ is the diffusion-model-based behavior cloning loss:

$$\mathcal{L}_d(\theta) = \mathbb{E}_{i, \epsilon, (s, a) \sim \mathcal{B}} \left\| \epsilon - \epsilon_\theta(\sqrt{\bar{\alpha}_i} a + \sqrt{1-\bar{\alpha}_i} \epsilon, s, i) \right\|^2$$

• The second term is a Q-guidance loss, favoring actions with high $Q$ defined by a double Q-network $Q_\phi$.
• $\alpha$ is data-adaptive: $\alpha = \frac{\eta}{\mathbb{E}[|Q_\phi(s,a)|]}$, with $\eta$ a hyperparameter.

This loss is optimized by reparameterizing $a^0$ as the end of the reverse diffusion chain, so policy improvement gradients propagate through all denoising steps. The Q-function is trained via standard TD learning with target networks.

Behavior cloning via the diffusion loss ensures the policy remains close to the data distribution (preserving support to mitigate extrapolation error), while Q-guidance enables improvement toward higher-reward actions within this support—avoiding common failure modes in classical offline RL.

3. Synergy of Sample-Based Regularization and Policy Improvement

Diffusion-QL's key insight is the simultaneous, unified training of the policy for both behavior cloning and optimality:

• Sample-based Regularization: The diffusion loss directly matches the sample distribution of the demonstrations—no auxiliary imitation policy or density estimation is needed.
• Policy Improvement: The Q-value guidance applies directly to the generated actions, with the diffusion chain ensuring gradient flow is not truncated. This coupling means the policy is only nudged toward higher-value actions to the extent that they are within (or nearby) the data coverage, sidestepping off-support action overestimation.

Ablations show that removing either loss term significantly degrades performance: both terms are necessary for robust and optimal policy learning.

4. Empirical Results and Benchmark Performance

Diffusion-QL achieves state-of-the-art results on a broad set of standard offline RL benchmarks:

• On D4RL Gym (MuJoCo) tasks, Diffusion-QL attains the highest average score ($88.0$), surpassing strong baselines such as CQL, IQL, TD3+BC, and Decision Transformer.
• In AntMaze tasks (long-horizon with sparse reward and suboptimal demonstrations), it achieves dramatic improvements (average $69.6$), excelling where other methods fail due to inadequate regularization or insufficient data support.
• For Adroit (human demos, distributional narrowness) and Kitchen (compositional, multi-stage), the model substantially exceeds prior work, confirming the practical utility of the approach in settings with complex, multi-strategy, or limited demonstration data.

These results are robust across high-dimensional, multi-modal action spaces and do not depend on artificially clean or single-strategy data—a frequent criticism of traditional offline RL results.

Empirical ablation and visualization confirm that diffusion-based policies avoid "mode collapse" and can represent all significant modes of the behavior policy, in contrast to alternative models (CVAE, Gaussian mixture) which underperform on multi-modal distributions.

5. Theoretical and Practical Implications

The diffusion policy paradigm fundamentally extends the feasible action distribution class for offline RL by:

• Capturing Multimodal Data: Any empirical distribution as sampled can be (in principle) exactly matched, eliminating the need for surrogate regularization terms (e.g. KLs, MMDs, explicit density estimation).
• Error Limiting Regularization: Joint training (loss above) anchors Q-guided policy search within empirical support, actively preventing out-of-distribution action evaluation—a key failure mode in previous methods.
• Data Flexibility: Diffusion policies are robust to heterogenous, multi-source datasets, supporting multiple behaviors, sub-policies, or human demonstrators.
• No Need for Separate Support Estimation: The diffusion loss naturally enforces sample regularization as part of the policy model, without separate density-ratio estimation.

Such flexibility is beneficial for both practical deployment in real-world systems and theoretical extension to more complex data modalities and control settings.

6. Algorithmic Considerations and Implementation

Implementing diffusion policies in offline RL demands:

• Training a denoising neural network $\epsilon_\theta$ (taking noisy actions, current state, diffusion timestep), typically a multi-layer perceptron with step, state, and action inputs.
• For action selection, an initial $a^N \sim \mathcal{N}(0, I)$ is iteratively denoised over $N$ steps, reconstructing $a^0$; gradients can be efficiently backpropagated through this chain.
• The Q-function $Q_\phi$ is generally a double Q-network with TD targets for stability.
• The per-task normalization factor $\alpha$ is set by the expected absolute Q-value in the dataset for numerical stability.

While diffusion policy inference is slower than direct Gaussian sampling due to multiple denoising steps, its improved policy quality, support coverage, and generalization have been empirically shown to outweigh computational cost on real tasks.

Potential computational savings can be sought using fast ODE solvers (DPM-solver, DDIM) or distillation to implicit policies, though with careful monitoring to avoid expressiveness loss.

7. Research Trajectory and Extensions

The adoption of diffusion policies in offline RL marks a paradigm shift in how expressivity, regularization, and optimal control are combined. Expected future directions include:

• Extension to hierarchical, temporally extended action spaces and richer observation modalities (e.g., vision, language).
• Generalization to online and multi-agent settings, with appropriately structured sample-based regularization.
• Hybridization with goal conditioning, model-based RL, or value-based regularizers.
• Theory of convergence, expressivity, and coverage guarantees in high-dimensional, real-world scenarios.
• Improving computational efficiency and integrating diffusion policy distillation for practical systems.

Diffusion policies, particularly in their joint regularization and reinforcement learning integration as exemplified in Diffusion-QL, have set new baselines for performance and reliability in offline learning from real-world, complex, and multimodal data settings.