Van Khoa Nguyen

Van Khoa Nguyen, Maciej Falkiewicz, Giangiacomo Mercatali et al.

Traditional molecule generation methods often rely on sequence- or graph-based representations, which can limit their expressive power or require complex permutation-equivariant architectures. This paper introduces a novel paradigm for learning molecule generative models based on functional representations. Specifically, we propose Molecular Implicit Neural Generation (MING), a diffusion-based model that learns molecular distributions in the function space. Unlike standard diffusion processes in the data space, MING employs a novel functional denoising probabilistic process, which jointly denoises information in both the function's input and output spaces by leveraging an expectation-maximization procedure for latent implicit neural representations of data. This approach enables a simple yet effective model design that accurately captures underlying function distributions. Experimental results on molecule-related datasets demonstrate MING's superior performance and ability to generate plausible molecular samples, surpassing state-of-the-art data-space methods while offering a more streamlined architecture and significantly faster generation times. The code is available at https://github.com/v18nguye/MING.

Van Khoa Nguyen, Yoann Boget, Frantzeska Lavda et al.

Learning graph generative models over latent spaces has received less attention compared to models that operate on the original data space and has so far demonstrated lacklustre performance. We present GLAD a latent space graph generative model. Unlike most previous latent space graph generative models, GLAD operates on a discrete latent space that preserves to a significant extent the discrete nature of the graph structures making no unnatural assumptions such as latent space continuity. We learn the prior of our discrete latent space by adapting diffusion bridges to its structure. By operating over an appropriately constructed latent space we avoid relying on decompositions that are often used in models that operate in the original data space. We present experiments on a series of graph benchmark datasets that demonstrates GLAD as the first equivariant latent graph generative method achieves competitive performance with the state of the art baselines.

Van Khoa Nguyen, Lionel Blondé, Alexandros Kalousis

Training free diffusion guidance provides a flexible way to leverage off-the-shelf classifiers without additional training. Yet, current approaches hinge on posterior approximations via Tweedie's formula, which often yield unreliable guidance, particularly in low-density regions. Stochastic optimal control (SOC), in contrast, provides principled posterior simulation but is prohibitively expensive for fast sampling. In this work, we reconcile the strengths of these paradigms by introducing Stein Diffusion Guidance (SDG), a novel training-free framework grounded in a surrogate SOC objective. We establish a theoretical bound on the value function, demonstrating the necessity of correcting approximate posteriors to faithfully reflect true diffusion dynamics. Leveraging Stein variational inference, SDG identifies the steepest descent direction that minimizes the Kullback-Leibler divergence between approximate and true posteriors. By incorporating a principled Stein correction mechanism and a novel running cost functional, SDG enables effective guidance in low-density regions. Experiments on molecular low-density sampling tasks suggest that SDG consistently surpasses standard training-free guidance methods, highlighting its potential for broader diffusion-based sampling beyond high-density regions.