Although iterative denoising (i.e., diffusion/flow) methods offer strong generative performance, they suffer from low generation efficiency, requiring hundreds of steps of network forward passes to simulate a single sample. Mitigating this requires taking larger step-sizes during simulation, thereby allowing one- or few-step generation. Recently proposed shortcut model learns larger step-sizes by enforcing alignment between its direction and the path defined by a base many-step flow-matching model through a self-consistency loss. However, its generation quality is significantly lower than the base model. In this paper, we interpret the self-consistency loss through the lens of optimal control by formulating the few-step generation as a controlled base generative process. This perspective enables us to develop a general cumulative self-consistency loss that penalizes the misalignment at both the current step and future steps along the trajectory. This encourages the model to take larger step-sizes that not only align with the base model at the current time step but also guide subsequent steps towards high-quality generation. Furthermore, we draw a connection between our approach and reinforcement learning, potentially opening the door to a new set of approaches for few-step generation. Extensive experiments show that we significantly improve one- and few-step generation quality under the same training budget.
