[Submitted on 8 Oct 2026 (v1), last revised 16 Oct 2026 (this version, v2)]
Abstract:Binary diffusion models typically require many function evaluations (NFEs) to generate high-quality samples, making inference costly. Reducing NFEs without sacrificing sample quality or relying on distillation or additional training remains challenging. Existing binary diffusion models define discrete one-step forward paths and derive reverse posteriors accordingly. In low-NFE cross-step sampling, they incorrectly approximate a true multi-step likelihood using a single-step transition, causing severe quality degradation. We propose Bernoulli Flow Models (BFM) to decouple generative dynamics from fixed discrete time steps. Instead of sequential one-step Markov diffusion chains, BFM defines a unified continuous global Bernoulli probability flow path between data and pure noise and derives analytical closed-form posterior transitions over arbitrary time intervals. Reducing the inference NFE therefore only requires re-evaluating this posterior on the new intervals rather than approximating skipped steps. This removes the structural training-inference mismatch of discrete chains and enables strictly self-consistent low-NFE sampling. Experiments show strong robustness under aggressive NFE reduction: on LSUN Churches 256×256, a 256-step-trained BFM achieves an FID of 9.22 with only 16 sampling steps, while the state-of-the-art discrete baseline degrades to 204.10. BFM also remains competitive with continuous and discrete generative baselines under standard full-step inference. These results establish BFM as a theoretically rigorous, self-consistent, and practical framework for fast binary data generation. Code is available at this https URL.
Submission history
From: Hao Mo [view email]
[v1] Thu, 8 Oct 2026 06:52:13 UTC (3,943 KB)
[v2] Fri, 16 Oct 2026 02:56:35 UTC (3,947 KB)
