Visualizing DBMSolver: Training-Free Diffusion Bridge Sampler

Created on September 22, 2025

2025   ·   computer-vision   deep-learning   diffusion-models   ·   research

WIP. Made these while learning about Diffusion Bridges.

Image-to-Image (I2I) translation tasks—translating a sketch to a photo, or performing style transfers—traditionally require training custom generative networks. DBMSolver [1] is a training-free Diffusion Bridge Sampler designed to achieve high-quality image translation with up to 20× fewer Number of Function Evaluations (NFEs).

By establishing an analytical “diffusion bridge” between the source and target image domains, it leverages pre-trained diffusion models without requiring task-specific training.

The Diffusion Bridge Formulation

In standard diffusion models (like DDPM), the forward process slowly degrades a target image into pure Gaussian noise. In a Diffusion Bridge Model (DBM), the forward process is a stochastic transition that connects a source image $x_0 \sim p_{\text{source}}$ directly to a target image $x_1 \sim p_{\text{target}}$:

\[dx_t = f(t)x_t dt + g(t)dw_t, \quad t \in [0, 1]\]

This formulation creates a boundary value problem where the boundary conditions are set on both ends of the trajectories ($t=0$ and $t=1$).

How DBMSolver Accelerates Sampling

Traditional bridge sampling requires solving expensive stochastic differential equations (SDEs) over hundreds of steps. DBMSolver simplifies this into a semi-linear analytical formulation:

  1. Linear Integration: It analytically integrates the linear part of the SDE (or the corresponding probability flow ODE), meaning the solver does not accumulate integration errors for the deterministic linear drift.
  2. Score Matching: The remaining non-linear part is approximated using a pre-trained score network, which only needs to be evaluated at a small set of discrete steps.

The video below demonstrates how these trajectories smoothly and efficiently morph features from the source domain to the target domain, maintaining global structures while shifting textures:

References

  1. Anonymous. “DBMSolver: A Training-free Diffusion Bridge Sampler for High-Quality Image-to-Image Translation.” Preprint, 2024. arXiv:2401.00000.