HyperDiffusionFields (HyDiF): Diffusion-Guided Hypernetworks for Learning Implicit Molecular Neural Fields

TL;DR

HyDiF proposes a diffusion-guided, field-based representation for molecules by learning Molecular Direction Fields (MDFs) which encode local geometry as a continuous vector field. A shared hypernetwork generates per-molecule Molecular Neural Fields (MNFs) that denoise MDFs through a denoising diffusion model, enabling both unconditional generation and structure-conditioned inpainting directly in function space. The MDf/MNF framework yields spatially localized features for downstream property prediction and demonstrates scalability to larger biomolecules such as proteins, addressing limitations of graph- and grid-based methods. Together, HyDiF unifies generation and representation learning in a single continuous-field model, offering a flexible, geometry-aware approach with practical implications for drug design and biomolecular modeling.

Abstract

We introduce HyperDiffusionFields (HyDiF), a framework that models 3D molecular conformers as continuous fields rather than discrete atomic coordinates or graphs. At the core of our approach is the Molecular Directional Field (MDF), a vector field that maps any point in space to the direction of the nearest atom of a particular type. We represent MDFs using molecule-specific neural implicit fields, which we call Molecular Neural Fields (MNFs). To enable learning across molecules and facilitate generalization, we adopt an approach where a shared hypernetwork, conditioned on a molecule, generates the weights of the given molecule's MNF. To endow the model with generative capabilities, we train the hypernetwork as a denoising diffusion model, enabling sampling in the function space of molecular fields. Our design naturally extends to a masked diffusion mechanism to support structure-conditioned generation tasks, such as molecular inpainting, by selectively noising regions of the field. Beyond generation, the localized and continuous nature of MDFs enables spatially fine-grained feature extraction for molecular property prediction, something not easily achievable with graph or point cloud based methods. Furthermore, we demonstrate that our approach scales to larger biomolecules, illustrating a promising direction for field-based molecular modeling.

Figures (12)

• Figure 1: HyperDiffusionFields (HyDiF) is a framework for learning molecular conformers capable of a variety of tasks, including unconditional generation of molecules, inpainting, and representation learning for molecular property prediction. Furthermore, HyDiF scales to larger biomolecules.
• Figure 2: Overview of the HyDiF architecture. A hypernetwork $H_\phi$ takes a noised direction field $\mathbf{F}_t(Q)$, query points $Q$, and noising timestep $t$, and produces the parameters $\theta$ of an MNF $\mathbf{F}_\theta$. The neural field is evaluated at the same query points to generate a denoised field, which is compared against the ground truth to compute the training loss. This enables HyDiF to model molecules in a spatially localized manner.
• Figure 3: Nine curated samples from unconditional generation. HyDiF generates chemically plausible and structurally diverse molecules when sampling unconditionally.
• Figure 4: Three molecules from the validation set and their corresponding inpaintings. Yellow denotes the region of the molecule we selected for inpainting. The above examples demonstrate the ability of HyDiF to inpaint effectively. We attribute this to HyDiF's ability to locally model conformers via MDFs. (a) replacement of the five-member ring with a six-member ring, and the replacement of a nitrogen (blue) with carbon (gray). (b) replacement of a carbon in a benzene ring with a nitrogen. (c) replacement of a branched chain with a non-branched chain.
• Figure 5: Training curves stratified by the distance from the query point to the nearest atom. Loss is tracked separately for five distance bins: very close, close, medium, far, and very far. The very close regime is the most challenging due to the high-frequency variation near the molecular surface. Loss in each bin initially decreases, then increases due to the progressive diffusion noise schedule.