  Recent advances in diffusion models have demonstrated their strong
capabilities in generating high-fidelity samples from complex distributions
through an iterative refinement process. Despite the empirical success of
diffusion models in motion planning and control, the model-free nature of these
methods does not leverage readily available model information and limits their
generalization to new scenarios beyond the training data (e.g., new robots with
different dynamics). In this work, we introduce Model-Based Diffusion (MBD), an
optimization approach using the diffusion process to solve trajectory
optimization (TO) problems without data. The key idea is to explicitly compute
the score function by leveraging the model information in TO problems, which is
why we refer to our approach as model-based diffusion. Moreover, although MBD
does not require external data, it can be naturally integrated with data of
diverse qualities to steer the diffusion process. We also reveal that MBD has
interesting connections to sampling-based optimization. Empirical evaluations
show that MBD outperforms state-of-the-art reinforcement learning and
sampling-based TO methods in challenging contact-rich tasks. Additionally,
MBD's ability to integrate with data enhances its versatility and practical
applicability, even with imperfect and infeasible data (e.g., partial-state
demonstrations for high-dimensional humanoids), beyond the scope of standard
diffusion models.
