Duc Kieu

Duc Kieu, Kien Do, Toan Nguyen et al.

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].

Kien Do, Duc Kieu, Toan Nguyen et al.

We propose a systematic training-free method to transform the probability flow of a "linear" stochastic process characterized by the equation X_{t}=a_{t}X_{0}+σ_{t}X_{1} into a straight constant-speed (SC) flow, reminiscent of Rectified Flow. This transformation facilitates fast sampling along the original probability flow via the Euler method without training a new model of the SC flow. The flexibility of our approach allows us to extend our transformation to inter-convert two posterior flows of two distinct linear stochastic processes. Moreover, we can easily integrate high-order numerical solvers into the transformed SC flow, further enhancing the sampling accuracy and efficiency. Rigorous theoretical analysis and extensive experimental results substantiate the advantages of our framework. Our code is available at this [https://github.com/clarken92/VFM||link].

Duc Kieu, Kien Do, Tuan Hoang et al.

Multi-domain translation (MDT) aims to learn translations between multiple domains, yet existing approaches either require fully aligned tuples or can only handle domain pairs seen in training, limiting their practicality and excluding many cross-domain mappings. We introduce universal MDT (UMDT), a generalization of MDT that seeks to translate between any pair of $K$ domains using only $K-1$ paired datasets with a central domain. To tackle this problem, we propose Diffusion Router (DR), a unified diffusion-based framework that models all central$\leftrightarrow$non-central translations with a single noise predictor conditioned on the source and target domain labels. DR enables indirect non-central translations by routing through the central domain. We further introduce a novel scalable learning strategy with a variational-bound objective and an efficient Tweedie refinement procedure to support direct non-central mappings. Through evaluation on three large-scale UMDT benchmarks, DR achieves state-of-the-art results for both indirect and direct translations, while lowering sampling cost and unlocking novel tasks such as sketch$\leftrightarrow$segmentation. These results establish DR as a scalable and versatile framework for universal translation across multiple domains.