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.

While most generative models show achievements in image data generation, few are developed for tabular data generation. Recently, due to success of large language models (LLM) in diverse tasks, they have also been used for tabular data generation. However, these methods do not capture the correct correlation between the features and the target variable, hindering their applications in downstream predictive tasks. To address this problem, we propose a LLM-based method with three important improvements to correctly capture the ground-truth feature-class correlation in the real data. First, we propose a novel permutation strategy for the input data in the fine-tuning phase. Second, we propose a feature-conditional sampling approach to generate synthetic samples. Finally, we generate the labels by constructing prompts based on the generated samples to query our fine-tuned LLM. Our extensive experiments show that our method significantly outperforms 10 SOTA baselines on 20 datasets in downstream tasks. It also produces highly realistic synthetic samples in terms of quality and diversity. More importantly, classifiers trained with our synthetic data can even compete with classifiers trained with the original data on half of the benchmark datasets, which is a significant achievement in tabular data generation.

We propose a novel approach to learn distributed representation for graph data. Our idea is to combine a recently introduced neural document embedding model with a traditional pattern mining technique, by treating a graph as a document and frequent subgraphs as atomic units for the embedding process. Compared to the latest graph embedding methods, our proposed method offers three key advantages: fully unsupervised learning, entire-graph embedding, and edge label leveraging. We demonstrate our method on several datasets in comparison with a comprehensive list of up-to-date state-of-the-art baselines where we show its advantages for both classification and clustering tasks.