# Latent Thermodynamic Flows: Unified Representation Learning and Generative Modeling of Temperature-Dependent Behaviors from Limited Data

arXiv: https://arxiv.org/abs/2507.03174 · HTML: https://mlsanity.com/paper/2507.03174/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 130 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Targeted free energy estimation via learned mappings](https://mlsanity.com/paper/2002.04913/) (2020)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [Transferable Boltzmann Generators](https://mlsanity.com/paper/2406.14426/) (2024)
- [Variational Encoding of Complex Dynamics](https://mlsanity.com/paper/1711.08576/) (2017)
- [Efficient mapping of phase diagrams with conditional Boltzmann Generators](https://mlsanity.com/paper/2406.12378/) (2024)
- [f-VAEs: Improve VAEs with Conditional Flows](https://mlsanity.com/paper/1809.05861/) (2018)
- [Reaction coordinate flows for model reduction of molecular kinetics](https://mlsanity.com/paper/2309.05878/) (2023)
- [Graph Neural Network-State Predictive Information Bottleneck (GNN-SPIB) approach for learning molecular thermodynamics and kinetics](https://mlsanity.com/paper/2409.11843/) (2024)
- [Using pretrained graph neural networks with token mixers as geometric featurizers for conformational dynamics](https://mlsanity.com/paper/2409.19838/) (2024)

## Abstract (arXiv)

Accurate characterization of the equilibrium distributions of complex molecular systems and their dependence on environmental factors such as temperature is essential for understanding thermodynamic properties and transition mechanisms. Projecting these distributions onto meaningful low-dimensional representations enables interpretability and downstream analysis. Recent advances in generative AI, particularly flow models such as Normalizing Flows (NFs), have shown promise in modeling such distributions, but their scope is limited without tailored representation learning. In this work, we introduce Latent Thermodynamic Flows (LaTF), an end-to-end framework that tightly integrates representation learning and generative modeling. LaTF unifies the State Predictive Information Bottleneck (SPIB) with NFs to simultaneously learn low-dimensional latent representations, referred to as Collective Variables (CVs), classify metastable states, and generate equilibrium distributions across temperatures beyond the training data. The two components of representation learning and generative modeling are optimized jointly, ensuring that the learned latent features capture the system's slow, important degrees of freedom while the generative model accurately reproduces the system's equilibrium behavior. We demonstrate LaTF's effectiveness across diverse systems, including a model potential, the Chignolin protein, and cluster of Lennard Jones particles, with thorough evaluations and benchmarking using multiple metrics and extensive simulations. Finally, we apply LaTF to a RNA tetraloop system, where despite using simulation data from only two temperatures, LaTF reconstructs the temperature-dependent structural ensemble and melting behavior, consistent with experimental and prior extensive computational results.