  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 the
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. Notably, our
proposed method enables one-step generation and inversion while also allowing
the use of additional steps to enhance generation quality or reduce
reconstruction error. Furthermore, by leveraging our model's bidirectional
consistency, we introduce a sampling strategy that can enhance FID while
preserving the generated image content. We further showcase our model's
capabilities in several downstream tasks, such as interpolation and inpainting,
and present demonstrations of potential applications, including blind
restoration of compressed images and defending black-box adversarial attacks.
