Bidirectional Consistency Models

Diffusion models (DMs) are capable of generating remarkably high-quality samples by iteratively denoising a random vector, a process that corresponds to moving along the probability flow ordinary differential equation (PF ODE). Interestingly, DMs can also invert an input image to noise by moving backward along the PF ODE, a key operation for downstream tasks such as interpolation and image editing. However, the iterative nature of this process restricts its speed, hindering its broader application. Recently, Consistency Models (CMs) have emerged to address this challenge by approximating the integral of the PF ODE, largely reducing the number of iterations. Yet, the absence of an explicit ODE solver complicates the inversion process. To resolve this, we introduce Bidirectional Consistency Model (BCM), which learns a single neural network that enables both forward and backward traversal along the PF ODE, efficiently unifying generation and inversion tasks within one framework. We can train BCM from scratch or tune it using a pretrained consistency model, wh ich reduces the training cost and increases scalability. We demonstrate that BCM enables one-step generation and inversion while also allowing the use of additional steps to enhance generation quality or reduce reconstruction error. We further showcase BCM's capability in downstream tasks, such as interpolation, inpainting, and blind restoration of compressed images. Notably, when the number of function evaluations (NFE) is constrained, BCM surpasses domain-specific restoration methods, such as I$^2$SB and Palette, in a fully zero-shot manner, offering an efficient alternative for inversion problems. Our code and weights are available at https://github.com/Mosasaur5526/BCM-iCT-torch.
Comment: 39 pages, 27 figures; a shorter version of this paper also appeared in the ICML 2024 Workshop on Structured Probabilistic Inference & Generative Modeling