Inverse problems, broadly defined as the task of estimating unknown input parameters of mathematical models from observed data, arise across a wide range of scientific and engineering disciplines. This talk presents deep generative approaches to solving such problems within a Bayesian inference framework, covering two complementary settings distinguished by whether the likelihood function is tractable. In the first half, we address the tractable likelihood setting, where Markov chain Monte Carlo (MCMC) has long served as the standard inference tool but suffers from slow mixing and high computational cost. We propose replacing MCMC with normalizing flow-based variational inference, which leverages GPU computing for substantially faster posterior approximation. We show, however, that naïve application of normalizing flows is insufficient: accurate posterior representation requires careful architectural choices—including mixture-based distributions to handle multimodality and tail-adaptive transformations to capture heavy-tailed behavior—as well as principled training strategies such as weight-adjusted fine-tuning to mitigate the mode-seeking bias of reverse KL divergence. In the second half, we turn to the intractable likelihood setting, where complex, high-dimensional, or semi-continuous data structures (such as spatial fields with excessive zeros) preclude explicit likelihood evaluation. Here, we employ denoising diffusion probabilistic models (DDPM) as emulators of the computer model output, and combine them with approximate Bayesian computation (ABC) in which a Siamese network extracts discriminative features to compute data-adaptive acceptance probabilities. Together, these methods extend the reach of principled Bayesian calibration to a broader class of scientifically important models.

Generative modeling has emerged as a powerful tool for molecular design and structure prediction, offering the ability for molecular discovery. However, challenges such as synthetic feasibility, novelty, diversity of generated molecules, and generalization ability of predictions remain critical for real-world applications, particularly in drug discovery. In this presentation, we introduce an overview of state-of-the-art generative models, including graph-based methods, generative flow networks, and diffusion methods, all aimed at addressing these challenges. First, we will show how generative modeling can facilitate the structural prediction of protein-ligand complexes and its expansion. Second, we focus on strategies that improve the synthesizability of generated molecules by incorporating chemical reaction templates, enabling the generation of novel compounds that are not only drug-like but also synthetically accessible. Third, large language models fine-tuned with drug-related data can be used to elucidating complex relationships between drugs, proteins, and diseases. Through case studies in drug design and broader molecular applications, we demonstrate how these generative modeling can help accelerate drug discovery, offering a pathway to more practical and innovative solutions across molecular discovery domains.