Binary Diffusion Probabilistic Model

TL;DR

BDPM addresses the mismatch between diffusion models and binary data by introducing transform-domain binary representations (MBPR and LBR) and XOR-based diffusion with binary cross-entropy loss. It demonstrates strong, data-efficient results on image-to-image translation tasks (super-resolution, inpainting, restoration) using a small 35.8M-parameter network, and competitive class-conditional generation on ImageNet-1k with 7 sampling steps. The approach offers faster convergence and reduced inference cost, enabling deployment on resource-constrained hardware, while acknowledging limitations and societal considerations around potential misuse.

Abstract

We propose the Binary Diffusion Probabilistic Model (BDPM), a generative framework specifically designed for data representations in binary form. Conventional denoising diffusion probabilistic models (DDPMs) assume continuous inputs, use mean squared error objectives and Gaussian perturbations, i.e., assumptions that are not suited to discrete and binary representations. BDPM instead encodes images into binary representations using multi bit-plane and learnable binary embeddings, perturbs them via XOR-based noise, and trains a model by optimizing a binary cross-entropy loss. These binary representations offer fine-grained noise control, accelerate convergence, and reduce inference cost. On image-to-image translation tasks, such as super-resolution, inpainting, and blind restoration, BDPM based on a small denoiser and multi bit-plane representation outperforms state-of-the-art methods on FFHQ, CelebA, and CelebA-HQ using a few sampling steps. In class-conditional generation on ImageNet-1k, BDPM based on learnable binary embeddings achieves competitive results among models with both low parameter counts and a few sampling steps.

Figures (14)

• Figure 1: Transform domain binary data representations. (a): MBPR of an image $\mathbf{I}_0$. The image is encoded using a bijective transform $\mathcal{T}$ into a tensor $\mathbf{x}_0$ of binary bit-planes, where MSB planes capture highly correlated structure and LSB planes contain decorrelated noise. (b): LBR obtained from an autoencoder architecture. The encoder outputs either quantized tokens which are subsequently binarized, or directly binarized latent vectors (e.g., via $\{-1, +1\}$ projections).
• Figure 2: Binary Diffusion training (left) and sampling (right) schemes.
• Figure 3: Relationship between the evaluation metrics and number of sampling steps on super-resolution task on FFHQ 256 $\times$ 256.
• Figure 4: Relationship between the evaluation metrics and number of sampling steps on inpainting task on FFHQ $512 \times 512$.
• Figure 5: Relationship between the evaluation metrics and number of sampling steps on blind image restoration task on CelebA 256 $\times$ 256.