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This paper addresses the challenge of accurately capturing nuclear quantum effects by framing them as a denoising problem, utilizing imaginary-time path integrals to connect quantum and classical representations. By training a denoiser on classical Boltzmann statistics and incorporating an analytic Gaussian component, the authors demonstrate that the quantum Boltzmann distribution can be achieved without the need for retraining across various quantum contexts. The key result shows that this method allows for exact transfer of properties such as temperature and boundary conditions, effectively linking generative modeling noise to quantum fluctuations.
A denoiser trained solely on classical statistics can accurately reproduce quantum Boltzmann distributions without retraining, revealing a profound connection between generative modeling and quantum fluctuations.
Nuclear quantum effects are rigorously captured by imaginary-time path integrals, which map the quantum Boltzmann distribution onto a ring polymer of classical replicas. Yet the nuclear masses, the coupling to the environment, and the boundary conditions of the path remain hard-wired in the simulation or the trained model, even though this quantum context enters the path measure only through a quadratic action known in closed form. Here we show that a denoiser trained on classical Boltzmann statistics alone, composed at sampling time with an analytic Gaussian component carrying the entire quantum context, yields the quantum Boltzmann distribution of the nuclei. Such a composition exists and is exact whenever the training noise does not exceed the intrinsic quantum uncertainty of the target ensemble, and it is invariant across all quantum contexts admitted by this bound. We show exact transfer across temperature, isotopic mass, dissipation strength, and the boundary conditions of the path in theory and in numerical experiments, without retraining. The last yields the end-to-end displacement and momentum distributions of a tagged nucleus from open imaginary-time paths. The same invariance extends in principle to the permuted boundary conditions of bosonic exchange, with the identical denoiser. In this view, the noise of generative modeling and the quantum fluctuations of the nuclei are two faces of the same quadratic structure.
