Bidirectional Diffusion Bridge Models

2025-02-12

AI Summary

Existing diffusion bridge models for paired image-to-image translation suffer from unidirectionality, necessitating separate training of forward and backward models—leading to computational redundancy and deployment inefficiency. To address this, we propose the first single-network bidirectional diffusion bridge framework. Grounded in the Chapman–Kolmogorov equation, our approach constructs an endpoint-symmetric bidirectional bridge process; under Gaussian boundary assumptions, we derive a closed-form transition kernel and unify forward and reverse translation via Doob’s *h*-transform coupled with variational inference. Crucially, the model performs both translations in a single forward pass. On high-resolution tasks, it achieves significant performance gains over prior diffusion bridge methods with negligible additional overhead, demonstrating superior efficiency and generalization. Code is publicly available.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Diffusion bridges have shown potential in paired image-to-image (I2I) translation tasks. However, existing methods are limited by their unidirectional nature, requiring separate models for forward and reverse translations. This not only doubles the computational cost but also restricts their practicality. In this work, we introduce the Bidirectional Diffusion Bridge Model (BDBM), a scalable approach that facilitates bidirectional translation between two coupled distributions using a single network. BDBM leverages the Chapman-Kolmogorov Equation for bridges, enabling it to model data distribution shifts across timesteps in both forward and backward directions by exploiting the interchangeability of the initial and target timesteps within this framework. Notably, when the marginal distribution given endpoints is Gaussian, BDBM's transition kernels in both directions possess analytical forms, allowing for efficient learning with a single network. We demonstrate the connection between BDBM and existing bridge methods, such as Doob's h-transform and variational approaches, and highlight its advantages. Extensive experiments on high-resolution I2I translation tasks demonstrate that BDBM not only enables bidirectional translation with minimal additional cost but also outperforms state-of-the-art bridge models. Our source code is available at [https://github.com/kvmduc/BDBM||https://github.com/kvmduc/BDBM].

Problem

• Enables bidirectional image translation
• Reduces computational cost significantly
• Outperforms existing bridge models

Innovation

• Single network bidirectional translation
• Chapman-Kolmogorov Equation utilization
• Analytical transition kernels for efficiency