Latent Diffusion-Based 3D Molecular Recovery from Vibrational Spectra

Abstract

Infrared (IR) spectroscopy, a type of vibrational spectroscopy, is widely used for molecular structure determination and provides critical structural information for chemists. However, existing approaches for recovering molecular structures from IR spectra typically rely on one-dimensional SMILES strings or two-dimensional molecular graphs, which fail to capture the intricate relationship between spectral features and three-dimensional molecular geometry. Recent advances in diffusion models have greatly enhanced the ability to generate molecular structures in 3D space. Yet, no existing model has explored the distribution of 3D molecular geometries corresponding to a single IR spectrum. In this work, we introduce IR-GeoDiff, a latent diffusion model that recovers 3D molecular geometries from IR spectra by integrating spectral information into both node and edge representations of molecular structures. We evaluate IR-GeoDiff from both spectral and structural perspectives, demonstrating its ability to recover the molecular distribution corresponding to a given IR spectrum. Furthermore, an attention-based analysis reveals that the model is able to focus on characteristic functional group regions in IR spectra, qualitatively consistent with common chemical interpretation practices.

Figures (10)

• Figure 1: Overview of the proposed IR-GeoDiff. A: Spectral features $S$ are extracted by a Transformer-based spectral classifier $\tau_\theta$. B: The encoder $\mathcal{E}_\phi$ maps molecular geometries into a latent representation $\mathbf{z_x}$, which is perturbed through a forward diffusion process and denoised by an equivariant network $\epsilon_\theta$ conditioned on the spectral features which are injected into node and edge representations via cross-attention. Finally, the decoder $\mathcal{D}_\delta$ reconstructs the 3D geometry from the denoised latent representation.
• Figure 2: Examples of molecules sampled under IR spectral conditions. For spectra, orange curves denote input IR spectra; purple curves denote spectra of sampled molecules. For atoms, hydrogen: white , carbon: gray, oxygen: red , nitrogen: blue .
• Figure 3: Visualisation of cross-attention between spectral features and molecular structure representations. A: Spectral–edge cross-attention highlighting functional-group-specific vibrational signatures. B: Spectral–atom cross-attention revealing associations between characteristic peaks and non-carbon heavy atoms. C: Spectral–atom cross-attention emphasising the carbon backbone.
• Figure 4: A: 2D histogram showing the joint distribution of $\mathrm{sim}_g$ and SIS, computed over 1,000 test spectra, with 50 sampled molecules per spectrum. B: Box plots of $\mathrm{sim}_g$ grouped by SIS ranges. C: Examples with high $\mathrm{sim}_g$ but low SIS. D: Examples of molecules with high SIS but low $\mathrm{sim}_g$. For spectra, orange curves denote input IR spectra; purple curves denote spectra of sampled molecules. For atoms, hydrogen: white , carbon: gray, oxygen: red , nitrogen: blue .
• Figure A1: Convergence of the mean Spectral Information Similarity (SIS) as the number of test IR spectra increases. The shaded region indicates the 95% confidence interval of the mean SIS. The curve stabilises after approximately 200 spectra, supporting the use of this subset for efficient and reliable evaluation. The result is based on one full sampling run (50,000 molecules in total).