# Combined Representation and Generation with Diffusive State Predictive Information Bottleneck

arXiv: https://arxiv.org/abs/2510.09784 · HTML: https://mlsanity.com/paper/2510.09784/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [Unified Generation, Reconstruction, and Representation: Generalized Diffusion with Adaptive Latent Encoding-Decoding](https://mlsanity.com/paper/2402.19009/) (2024)
- [Generative artificial intelligence for computational chemistry: a roadmap to predicting emergent phenomena](https://mlsanity.com/paper/2409.03118/) (2024)

## Built on by (most cited first, 1 of 1)

- [Differentiable free energy surface: a variational approach to directly observing rare events using generative deep-learning models](https://mlsanity.com/paper/2604.09769/) (2026)

## Abstract (arXiv)

Generative modeling becomes increasingly data-intensive in high-dimensional spaces. In molecular science, where data collection is expensive and important events are rare, compression to lower-dimensional manifolds is especially important for various downstream tasks, including generation. We combine a time-lagged information bottleneck designed to characterize molecular important representations and a diffusion model in one joint training objective. The resulting protocol, which we term Diffusive State Predictive Information Bottleneck (D-SPIB), enables the balancing of representation learning and generation aims in one flexible architecture. Additionally, the model is capable of combining temperature information from different molecular simulation trajectories to learn a coherent and useful internal representation of thermodynamics. We benchmark D-SPIB on multiple molecular tasks and showcase its potential for exploring physical conditions outside the training set.