Minimum-Excess-Work Guidance

We propose a regularization framework inspired by thermodynamic work for guiding pre-trained probability flow generative models (e.g., continuous normalizing flows or diffusion models) by minimizing excess work, a concept rooted in statistical mechanics and with strong conceptual connections to optimal transport. Our approach enables efficient guidance in sparse-data regimes common to scientific applications, where only limited target samples or partial density constraints are available. We introduce two strategies: Path Guidance for sampling rare transition states by concentrating probability mass on user-defined subsets, and Observable Guidance for aligning generated distributions with experimental observables while preserving entropy. We demonstrate the framework's versatility on a coarse-grained protein model, guiding it to sample transition configurations between folded/unfolded states and correct systematic biases using experimental data. The method bridges thermodynamic principles with modern generative architectures, offering a principled, efficient, and physics-inspired alternative to standard fine-tuning in data-scarce domains. Empirical results highlight improved sample efficiency and bias reduction, underscoring its applicability to molecular simulations and beyond.

@article{kolloff2025_2505.13375,
  title={ Minimum-Excess-Work Guidance },
  author={ Christopher Kolloff and Tobias Höppe and Emmanouil Angelis and Mathias Jacob Schreiner and Stefan Bauer and Andrea Dittadi and Simon Olsson },
  journal={arXiv preprint arXiv:2505.13375},
  year={ 2025 }
}