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Bernoulli Flow Models: Self-Consistent Generative Modeling for Binary Data

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Diffusion theory and learned samplers

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Proposes Bernoulli Flow Models, a continuous Bernoulli probability path with closed-form arbitrary-interval posteriors, enabling training-free low-NFE sampling from a single binary diffusion checkpoint.

Problem

Binary diffusion models need many function evaluations for high-quality sampling, and reducing NFEs after training is unreliable because cross-step reverse posteriors are approximated by one-step transitions.

Approach

Define a global continuous Bernoulli flow path between data and uniform noise, derive closed-form marginal, transition and posterior distributions over arbitrary time intervals, and train a network to predict X_0 with BCE so that changing the inference grid just re-evaluates the analytical posterior.

Key results

• On LSUN Churches 256x256, a 256-step-trained BFM reaches FID 9.22 with 16 sampling steps, versus 204.10 for BLD.
• Under matched 64-step reproduction, BFM achieves FID 5.86 vs 6.22 for reproduced BLD on LSUN Bedrooms and 10.87 vs 11.46 on FFHQ.
• On binarized MNIST, BFM reports FID 0.42, described as the best among evaluated models.

Surprising findings

• The BLD official code uses only the last-step noise parameter for cross-step updates, which the authors argue is an approximation that degrades low-NFE sampling.

Limitations

• Evaluation limited to image generation and a scientific Ising benchmark, per the authors.
• Reported BLD baseline numbers are reproductions rather than originally reported results; the authors note the comparison is not fully controlled against the original checkpoints.
• FID varies slightly more across schedulers for BFM than for BLD.

Experimental setup

Datasets: LSUN Bedrooms LSUN Churches FFHQ Binarized MNIST Ising model samples (Wolff cluster)

Benchmarks: LSUN-Bedrooms 256x256 LSUN-Churches 256x256 FFHQ 256x256 Binarized MNIST Ising model magnetization

Metrics: FID Precision Recall

Baselines: BLD StyleGAN LDM-4 Patch-DM VQ-LCMD D3PM VQ-Diffusion

Builds on: Binary Latent Diffusion DDPM DDIM Analog Bits

Closest papers by meaning

• Towards Non-Asymptotic Convergence for Diffusion-Based Generative Models (ICLR 2024 · similarity 0.89)
• Systematic Hazard Sampling: Minimal-Variance Inference for Discrete Diffusion and Flow Models (NeurIPS 2026 · similarity 0.88)
• Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms (NeurIPS 2025 · similarity 0.88)
• Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Models (NeurIPS 2024 · similarity 0.88)
• Discrete Flow Matching (NeurIPS 2024 · similarity 0.88)
• Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling (NeurIPS 2024 · similarity 0.88)