Learning Diffusion-Bridge Flow Maps with Continuous-time Consistency

Diffusion Bridge Models (DBMs) provide a diffusion-based framework for image-to-image (I2I) translation. However, high-quality sampling often requires tens of costly neural-network evaluations. Recent consistency-based approaches accelerate sampling by learning direct mappings from intermediate bridge states ${\mathbf{x}}_t$ to the data endpoint ${\mathbf{x}}_0$, but do not learn the entire bridge flow. In this work, we develop a single consistency model that represents the entire finite-time bridge flow, mapping any intermediate state ${\mathbf{x}}_t$ directly to any earlier state ${\mathbf{x}}_s$. Learning the full bridge flow poses two main challenges: how to represent the flow, and how to train it stably in continuous time. We address these issues by using the exact solution of the bridge PF-ODE to structure the learned map, and by deriving a bridge-specific sign correction that prevents the continuous-time update from amplifying flow-map inconsistency. On held-out ImageNet-512 super-resolution and deblurring, BFM reduces FID-VAE over reproduced CDBM by $39.5$ and $23.2$, respectively, at the same 4-NFE budget; at 8 NFEs, it reaches FID-VAE comparable to DBMSolver using 20-30 NFEs.