Stochastic Flow Matching for Resolving Small-Scale Physics
Stathi Fotiadis, Noah Brenowitz, Tomas Geffner, Yair Cohen, Michael, Pritchard, Arash Vahdat, Morteza Mardani
TL;DR
This paper introduces stochastic flow matching, a novel method for super-resolving small-scale physical details by combining deterministic encoding with stochastic flow generation, effectively handling multi-scale dynamics and limited data.
Contribution
The paper proposes a new stochastic flow matching framework that encodes inputs into a latent distribution and uses flow matching to generate small-scale physics, addressing key challenges in physical super-resolution.
Findings
Outperforms existing methods like conditional diffusion and flows.
Successfully applied to weather and PDE datasets.
Effectively captures uncertainty and multi-scale dynamics.
Abstract
Conditioning diffusion and flow models have proven effective for super-resolving small-scale details in natural images.However, in physical sciences such as weather, super-resolving small-scale details poses significant challenges due to: (i) misalignment between input and output distributions (i.e., solutions to distinct partial differential equations (PDEs) follow different trajectories), (ii) multi-scale dynamics, deterministic dynamics at large scales vs. stochastic at small scales, and (iii) limited data, increasing the risk of overfitting. To address these challenges, we propose encoding the inputs to a latent base distribution that is closer to the target distribution, followed by flow matching to generate small-scale physics. The encoder captures the deterministic components, while flow matching adds stochastic small-scale details. To account for uncertainty in the deterministic…
Peer Reviews
Decision·Submitted to ICLR 2025
- The authors conducted comprehensive experiments on both synthetic and real-world datasets. - The paper includes ablation studies and spectral analysis, which reveal the impact of different architectural choices and underscore SFM's robustness in capturing high-frequency details. - The dynamic adjustment of noise levels based on the encoder’s prediction error provides a robust method to balance deterministic and stochastic data components.
- It is not clear why the method is named and formalized as "flow matching" because the actual implementation is based on EDM. The perturbation and the denoising model both follow the diffusion custom instead of flow matching. Please justify whether the method especially the probability path is closer to flow matching or diffusion. - In Algorithm 2. the inputs to the denoising model $\mathcal{D}_\theta$ are $(x, t)$ but elsewhere $(x, \sigma)$. This may lead to confusion on how the adaptive noi
1. The overall idea for cross-modality image translation is promising. 2. The proposed stochastic encoder-denoiser pipeline is interesting. 3. Extensive Experiments illustrate the effectiveness of the proposed method, and the results on most datasets are good.
1. If the authors want to add uncertainty to the deterministic part, maybe the better way is to apply approaches like VAE to output both mean and variance (the downscale layers can be removed if there is no resolution change). Using VAE can also avoid the tuning of noise scales. 2. Also, calling this method "stochastic flow matching" is somehow improper, since the flow matching is usually an ODE. Note that the original flow matching also accepts noise input. Adding the "stochastic" to "flow ma
1. The presentation is apparent and the description of the proposed methodology is accurate and easy to follow. 2. The figure and quantitative comparisons are good, the experiment is sufficiently adequate, the experimental setup is described in detail with methodological details and it should be easily reproducible.
1. The problem of novelty, due to the well-known connection between flow matching and diffusion modeling. The approach proposed in this paper seems to resemble CorrDiff. Although the authors emphasize the difference in Section 4.4. They claim that CorrDiff is trained in two stages, i.e., the regression encoder is trained first and the diffusion of the residual components is trained afterwards. In contrast, it seems that in this paper, the two components are only trained jointly, and the final lo
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Taxonomy
TopicsComputational Physics and Python Applications · Reservoir Engineering and Simulation Methods · Parallel Computing and Optimization Techniques
MethodsDiffusion · Balanced Selection