Dang H. Nguyen

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].

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.

Kien Do, Dung Nguyen, Hung Le et al.

In this paper, we study the "dataset bias" problem from a statistical standpoint, and identify the main cause of the problem as the strong correlation between a class attribute u and a non-class attribute b in the input x, represented by p(u|b) differing significantly from p(u). Since p(u|b) appears as part of the sampling distributions in the standard maximum log-likelihood (MLL) objective, a model trained on a biased dataset via MLL inherently incorporates such correlation into its parameters, leading to poor generalization to unbiased test data. From this observation, we propose to mitigate dataset bias via either weighting the objective of each sample n by \frac{1}{p(u_{n}|b_{n})} or sampling that sample with a weight proportional to \frac{1}{p(u_{n}|b_{n})}. While both methods are statistically equivalent, the former proves more stable and effective in practice. Additionally, we establish a connection between our debiasing approach and causal reasoning, reinforcing our method's theoretical foundation. However, when the bias label is unavailable, computing p(u|b) exactly is difficult. To overcome this challenge, we propose to approximate \frac{1}{p(u|b)} using a biased classifier trained with "bias amplification" losses. Extensive experiments on various biased datasets demonstrate the superiority of our method over existing debiasing techniques in most settings, validating our theoretical analysis.

Minh-Ngoc Tran, Dang H. Nguyen, Duy Nguyen

Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational parameter space is Euclidean, which hinders the potential broad application of VB methods. This paper extends the scope of VB to the case where the variational parameter space is a Riemannian manifold. We develop an efficient manifold-based VB algorithm that exploits both the geometric structure of the constraint parameter space and the information geometry of the manifold of VB approximating probability distributions. Our algorithm is provably convergent and achieves a convergence rate of order $\mathcal O(1/\sqrt{T})$ and $\mathcal O(1/T^{2-2ε})$ for a non-convex evidence lower bound function and a strongly retraction-convex evidence lower bound function, respectively. We develop in particular two manifold VB algorithms, Manifold Gaussian VB and Manifold Neural Net VB, and demonstrate through numerical experiments that the proposed algorithms are stable, less sensitive to initialization and compares favourably to existing VB methods.