Moving data points along straight paths instead of curves

Generative models typically move data from noise to realistic samples along curved paths—diffusion models take many steps, flows require specialized architectures. This work reformulates generation as a control problem solvable via linear programming, yielding value-driven transport (VDT) policies that move data in straight lines. The method is faster to run, naturally handles conditioning and guidance techniques from diffusion models, and shows competitive performance across standard benchmarks.