FARFlow: Learning Finite-Span Flow Maps for Few-Step Protein Backbone Generation

Diffusion- and flow-based models generate high-quality protein backbones, but reducing sampling cost requires reliable predictions over finite time intervals. We introduce Finite-Span Anchoring and Replay Flow (FARFlow), a solution-function-based method for few-step $C_o$ backbone generation. FARFlow separates the requested prediction span from the input noise level through an unscaled, zero-anchored additive condition. This representation leaves the local-velocity condition unchanged at zero span while providing a smoothly varying correction for finite-span requests. Direct endpoint anchoring supervises predictions using paired clean backbones, and fresh-noise replay extends this supervision to inputs reconstructed from predicted endpoints. Under constrained budgets, FARFlow achieves higher designability than compared baselines while retaining reasonable structural diversity. On the standard multi-length benchmark, it maintains high generation quality across all evaluated lengths, achieving aggregate designability comparable to higher-budget multi-step models with substantially fewer network evaluations.