Delta Flow Matching for Robot Foundation Models

Flow matching is a common generative recipe for robot foundation models. Vision-language-action models (VLAs) generate action chunks, while world-action models (WAMs) additionally generate future visual states. Both start generation from a fixed Gaussian prior, despite temporal continuity between past and future states and actions. This requires costly training and iterative sampling, especially for WAMs with an additional visual branch. We introduce Delta-flow, which constructs the source from recent history with mild noise rather than from a fixed Gaussian prior. This moves the source closer to the target, reducing transport to a small residual Delta that can be learned efficiently and enables single-step inference. We integrate Delta-flow into the VLA policy π0.5 and the WAM policies ImageWAM and Fast-WAM. On LIBERO, ImageWAM reaches 90% success in one epoch rather than six, and Fast-WAM reaches 95% in two epochs rather than eight. With LoRA fine-tuning, π0.5 exceeds its baseline's five-epoch performance after one epoch. Single-step inference gives 1.54×, 2.49×, and 4.45× speedups on π0.5, ImageWAM, and Fast-WAM, respectively. It preserves action smoothness, achieving a 4.5× reduction in action jerk compared with one-step Gaussian sampling. Delta-flow reaches state-of-the-art generalization performance on LIBERO-Plus. Action-history sources can be applied to pretrained WAM policies without retraining. Replacing the Gaussian action source at inference largely preserves task success with a single sampling step and can slightly improve it. We further study how action representation and visual information in action learning affect history-to-future prediction in Delta-flow. These results show that Delta-flow is simple yet effective, improving the efficiency and generalization of robot foundation models.