  Flow matching is a powerful framework for generating high-quality samples in
various applications, especially image synthesis. However, the intensive
computational demands of these models, especially during the finetuning process
and sampling processes, pose significant challenges for low-resource scenarios.
This paper introduces Bellman Optimal Stepsize Straightening (BOSS) technique
for distilling flow-matching generative models: it aims specifically for a
few-step efficient image sampling while adhering to a computational budget
constraint. First, this technique involves a dynamic programming algorithm that
optimizes the stepsizes of the pretrained network. Then, it refines the
velocity network to match the optimal step sizes, aiming to straighten the
generation paths. Extensive experimental evaluations across image generation
tasks demonstrate the efficacy of BOSS in terms of both resource utilization
and image quality. Our results reveal that BOSS achieves substantial gains in
efficiency while maintaining competitive sample quality, effectively bridging
the gap between low-resource constraints and the demanding requirements of
flow-matching generative models. Our paper also fortifies the responsible
development of artificial intelligence, offering a more sustainable generative
model that reduces computational costs and environmental footprints. Our code
can be found at https://github.com/nguyenngocbaocmt02/BOSS.
