Beyond the History Span: State-Guided Span Expansion for Efficient Diffusion Inference

Diffusion Transformers require repeated model evaluations across many sampling steps, resulting in substantial computational overhead. A recent line of methods reduces this cost by replacing selected model evaluations with linear forecasts. These methods represent the Transformer velocity at each skipped step as a linear combination of historical velocities. However, forecasting errors grow over consecutive forecast steps because such forecasts are confined to the linear span of historical velocities and cannot represent velocity components outside this span. To overcome this limitation, we propose state-guided span expansion (SGSE), which expands the historical velocity span using a complementary direction derived from the sampling state. Specifically, we forecast a sampling state and map it through the inverse sampler update to obtain a state-implied velocity. The out-of-span component of this state-implied velocity is directionally similar to the corresponding component of the full-Transformer velocity, providing complementary information unavailable from historical velocities alone. SGSE incorporates this complementary direction into velocity forecasting, expanding the representational space beyond the historical span and thus reducing forecasting error. Experiments on image and video generation demonstrate that SGSE consistently outperforms existing forecasting-based acceleration methods.