# Consistency Diffusion Bridge Models

arXiv: https://arxiv.org/abs/2410.22637 · HTML: https://mlsanity.com/paper/2410.22637/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 57 of its 73 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 57)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)

## Built on by (most cited first, 23 of 23)

- [Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistency](https://mlsanity.com/paper/2510.08431/) (2025)
- [OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offs](https://mlsanity.com/paper/2412.09465/) (2024)
- [Inverse Bridge Matching Distillation](https://mlsanity.com/paper/2502.01362/) (2025)
- [InfoBridge: Mutual Information estimation via Bridge Matching](https://mlsanity.com/paper/2502.01383/) (2025)
- [System-Embedded Diffusion Bridge Models](https://mlsanity.com/paper/2506.23726/) (2025)
- [Schr"odinger Bridge Consistency Trajectory Models for Speech Enhancement](https://mlsanity.com/paper/2507.11925/) (2025)
- [Diffusion Bridge Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/2509.19078/) (2025)
- [Midpoint Generative Models](https://mlsanity.com/paper/2605.29920/) (2026)
- [One-Step Residual Shifting Diffusion for Image Super-Resolution via Distillation](https://mlsanity.com/paper/2503.13358/) (2025)
- [Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysis](https://mlsanity.com/paper/2509.24531/) (2025)
- [Adaptive Domain Shift in Diffusion Models for Cross-Modality Image Translation](https://mlsanity.com/paper/2601.18623/) (2026)
- [An Ordinary Differential Equation Sampler with Stochastic Start for Diffusion Bridge Models](https://mlsanity.com/paper/2412.19992/) (2024)
- [A Unified and Fast-Sampling Diffusion Bridge Framework via Stochastic Optimal Control](https://mlsanity.com/paper/2505.21528/) (2025)
- [Towards General Modality Translation with Contrastive and Predictive Latent Diffusion Bridge](https://mlsanity.com/paper/2510.20819/) (2025)
- [FluxFlow: Conservative Flow-Matching for Astronomical Image Super-Resolution](https://mlsanity.com/paper/2605.03749/) (2026)
- [Learning Stochastic Bridges for Video Object Removal via Video-to-Video Translation](https://mlsanity.com/paper/2601.12066/) (2026)
- [Efficient Hybrid SE(3)-Equivariant Visuomotor Flow Policy via Spherical Harmonics for Robot Manipulation](https://mlsanity.com/paper/2603.23227/) (2026)
- [Entropy Across the Bridge: Conditional-Marginal Discretization for Flow and Schr"odinger Samplers](https://mlsanity.com/paper/2605.16126/) (2026)
- [Neural Bridge Processes](https://mlsanity.com/paper/2508.07220/) (2025)
- [EarthBridge: A Solution for 4th Multi-modal Aerial View Image Challenge Translation Track](https://mlsanity.com/paper/2603.06753/) (2026)
- [DBMSolver: A Training-free Diffusion Bridge Sampler for High-Quality Image-to-Image Translation](https://mlsanity.com/paper/2605.05889/) (2026)
- [GoodDiffusion: Proactive Copyright Protection for Diffusion Bridge Models via Learnable Sample-specific Signatures](https://mlsanity.com/paper/2606.29759/) (2026)
- [PRISM: Principled Reference Identification for Schrodinger Bridge Model](https://mlsanity.com/paper/2608.06893/) (2026)

## Abstract (arXiv)

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of generative modeling that builds stochastic processes between fixed data endpoints based on a reference diffusion process, have achieved empirical success across tasks with coupled data distribution, such as image-to-image translation. However, DDBM's sampling process typically requires hundreds of network evaluations to achieve decent performance, which may impede their practical deployment due to high computational demands. In this work, inspired by the recent advance of consistency models in DMs, we tackle this problem by learning the consistency function of the probability-flow ordinary differential equation (PF-ODE) of DDBMs, which directly predicts the solution at a starting step given any point on the ODE trajectory. Based on a dedicated general-form ODE solver, we propose two paradigms: consistency bridge distillation and consistency bridge training, which is flexible to apply on DDBMs with broad design choices. Experimental results show that our proposed method could sample 4× to 50× faster than the base DDBM and produce better visual quality given the same step in various tasks with pixel resolution ranging from 64 × 64 to 256 × 256, as well as supporting downstream tasks such as semantic interpolation in the data space.