Structured Diffusion Bridges: Inductive Bias for Denoising Diffusion Bridges

Modality translation is inherently under-constrained, as multiple cross-modal mappings may yield the same marginals. Recent work has shown that diffusion bridges are effective for this task. However, most existing approaches rely on fully paired datasets, thereby imposing a single data-driven constraint. We propose a diffusion-bridge framework that characterizes the space of admissible solutions and restricts it via alignment constraints, treating paired supervision as an optional heuristic rather than a prerequisite. We validate our method on synthetic and real modality translation benchmarks across unpaired, semi-paired, and paired regimes, showing consistent performance across supervision levels. Notably, it achieves near fully-paired quality with a substantial relaxation in pairing requirements, and remaining applicable in the unpaired regime. These results highlight diffusion bridges as a flexible foundation for modality translation beyond fully paired data.

Machine learning systems frequently require translation between different data types, such as images, signals, text, or other measurements. This task is challenging because multiple valid translations may exist, with different outputs corresponding equally well to the same input. Most existing methods assume access to numerous perfectly matched examples, where each input is paired with its correct output. However, in practical scenarios, such paired data are often costly, incomplete, or unavailable. This paper presents a more versatile approach to data type translation. Rather than relying exclusively on fully paired datasets, the proposed method can utilize weaker forms of guidance when available and remains effective in the absence of paired examples. The method is evaluated on both controlled and real-world benchmarks, demonstrating strong performance across unpaired, partially paired, and fully paired settings. Notably, it achieves performance comparable to fully paired methods while requiring significantly fewer paired examples.