Training-Free Adaptation of Diffusion Models via Doob's $h$-Transform
arXiv:2602.16198v1 Announce Type: new Abstract: Adaptation methods have been a workhorse for unlocking the transformative power of pre-trained diffusion models in diverse applications. Existing approaches often abstract adaptation objectives as a reward function and steer diffusion models to generate high-reward samples. However, these approaches can incur high computational overhead due to additional training, or rely on stringent assumptions on the reward such as differentiability. Moreover, despite their empirical success, theoretical justification and guarantees are seldom established. In this paper, we propose DOIT (Doob-Oriented Inference-time Transformation), a training-free and computationally efficient adaptation method that applies to generic, non-differentiable rewards. The key framework underlying our method is a measure transport formulation that seeks to transport the pre-trained generative distribution to a high-reward target distribution. We leverage Doob's $h$-transfo
arXiv:2602.16198v1 Announce Type: new Abstract: Adaptation methods have been a workhorse for unlocking the transformative power of pre-trained diffusion models in diverse applications. Existing approaches often abstract adaptation objectives as a reward function and steer diffusion models to generate high-reward samples. However, these approaches can incur high computational overhead due to additional training, or rely on stringent assumptions on the reward such as differentiability. Moreover, despite their empirical success, theoretical justification and guarantees are seldom established. In this paper, we propose DOIT (Doob-Oriented Inference-time Transformation), a training-free and computationally efficient adaptation method that applies to generic, non-differentiable rewards. The key framework underlying our method is a measure transport formulation that seeks to transport the pre-trained generative distribution to a high-reward target distribution. We leverage Doob's $h$-transform to realize this transport, which induces a dynamic correction to the diffusion sampling process and enables efficient simulation-based computation without modifying the pre-trained model. Theoretically, we establish a high probability convergence guarantee to the target high-reward distribution via characterizing the approximation error in the dynamic Doob's correction. Empirically, on D4RL offline RL benchmarks, our method consistently outperforms state-of-the-art baselines while preserving sampling efficiency.
Executive Summary
This paper introduces DOIT, a training-free and computationally efficient adaptation method for unlocking the transformative power of pre-trained diffusion models. Building on Doob's $h$-transform, DOIT seeks to transport the pre-trained generative distribution to a high-reward target distribution through measure transport formulation. This approach enables efficient simulation-based computation without modifying the pre-trained model and establishes a high probability convergence guarantee to the target distribution. Empirical results on D4RL offline RL benchmarks demonstrate the superiority of DOIT over state-of-the-art baselines while preserving sampling efficiency. This innovative method has far-reaching implications for various applications, including computer vision, natural language processing, and robotics.
Key Points
- ▸ DOIT is a training-free and computationally efficient adaptation method for pre-trained diffusion models.
- ▸ DOIT leverages Doob's $h$-transform for measure transport formulation and dynamic correction of the diffusion sampling process.
- ▸ The method establishes a high probability convergence guarantee to the target distribution through characterization of the approximation error in the dynamic Doob's correction.
Merits
Strength
DOIT's training-free and computationally efficient design enables adaptation of pre-trained diffusion models without incurring high computational overhead, making it a practical solution for various applications.
Strength
The method's high probability convergence guarantee provides a theoretical justification and guarantee, addressing a significant limitation of existing adaptation approaches.
Demerits
Limitation
The paper assumes the availability of a pre-trained diffusion model, which may not be the case in certain scenarios, limiting the applicability of DOIT.
Limitation
The method's performance may be sensitive to the choice of reward function and target distribution, requiring careful selection and tuning for optimal results.
Expert Commentary
The innovative approach of DOIT and its associated theoretical justification are significant contributions to the field of adaptation methods for pre-trained diffusion models. The method's practical implications for computer vision, natural language processing, and robotics are substantial, and its policy implications for decision-making and policy development are considerable. However, the limitations of the method, including its reliance on pre-trained models and sensitivity to reward function and target distribution selection, require careful consideration and further research.
Recommendations
- ✓ Future research should focus on extending DOIT to handle more complex scenarios, such as multi-task adaptation and adaptation with diverse reward functions.
- ✓ Further investigation into the sensitivity of DOIT's performance to reward function and target distribution selection is necessary to ensure optimal results in various applications.
