# METALICA: METAdynamics and repLICA exchange for enhanced diffusion sampling

arXiv: https://arxiv.org/abs/2609.17823 · HTML: https://mlsanity.com/paper/2609.17823/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 10 of 10)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Particle Denoising Diffusion Sampler](https://mlsanity.com/paper/2402.06320/) (2024)
- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Accelerated Parallel Tempering via Neural Transports](https://mlsanity.com/paper/2502.10328/) (2025)
- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [Enhanced Diffusion Sampling: Efficient Rare Event Sampling and Free Energy Calculation with Diffusion Models](https://mlsanity.com/paper/2602.16634/) (2026)
- [CREPE: Controlling Diffusion with Replica Exchange](https://mlsanity.com/paper/2509.23265/) (2025)
- [Unlocking hidden biomolecular conformational landscapes in diffusion models at inference time](https://mlsanity.com/paper/2512.03312/) (2025)

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

- [ENCORE: Exact Non-equilibrium COntrol with Replica Exchange for Diffusion Generation](https://mlsanity.com/paper/2610.02538/) (2026)

## Abstract (arXiv)

Many proteins function through transitions between conformational states, yet rare states are rarely sampled by diffusion models trained on an equilibrium ensemble, demanding better sampling methods. We introduce METALICA, which implements Metadynamics on a pretrained diffusion model via Replica Exchange. It accumulates a bias potential along a Collective Variable, repels new samples from previous ones through biased sampling, and reweights samples onto the unbiased distribution. METALICA holds one replica per diffusion level, forming a Markov Chain that evolves through inter-replica communication and is refined in place as the bias grows. METALICA is the dual of sequential control, in which Sequential Monte Carlo parallelizes the sampler over a batch of particles. Parallelism over the levels of the diffusion-time schedule instead allows METALICA to generate samples from long chains, essential for the discovery of rare events, with accuracy set by run length rather than by the memory available. We validate on a bimodal target with known free energies, then apply METALICA to the unfolding of a protein. At a budget for which sequential control yields no unfolded structure, METALICA populates the basin and resolves a second free energy minimum.