TL;DR
This paper introduces Interaction Field Matching (IFM), a generalization of electrostatic field matching that overcomes previous limitations by incorporating more complex interaction fields, demonstrated on toy and image data transfer tasks.
Contribution
It proposes a novel generalization of electrostatic field matching that includes complex interaction fields, addressing modeling challenges in the original EFM approach.
Findings
Effective on toy data transfer problems
Improves modeling of complex interaction fields
Code available for reproducibility
Abstract
Electrostatic field matching (EFM) has recently appeared as a novel physics-inspired paradigm for data generation and transfer using the idea of an electric capacitor. However, it requires modeling electrostatic fields using neural networks, which is non-trivial because of the necessity to take into account the complex field outside the capacitor plates. In this paper, we propose Interaction Field Matching (IFM), a generalization of EFM which allows using general interaction fields beyond the electrostatic one. Furthermore, inspired by strong interactions between quarks and antiquarks in physics, we design a particular interaction field realization which solves the problems which arise when modeling electrostatic fields in EFM. We show the performance on a series of toy and image data transfer problems. Our code is available at https://github.com/justkolesov/InteractionFieldMatching
Peer Reviews
Decision·ICLR 2026 Poster
1. The paper proposes a novel physics-inspired framework that addresses key limitations of existing EFM methods. IFM produces nearly straight field lines and effectively covers the target distribution, which is significant both theoretically and practically. 2. The authors provide solid theoretical foundations, including proofs of flow conservation properties and mathematical analysis of field line behavior. Theorems and lemmas in the appendix guarantee the correctness of the method. 3. The expe
1. Although the paper mentions potential numerical precision issues in high dimensions, it lacks systematic analysis of their practical impact. In real applications, when dimension D is large, this issue could cause algorithm instability or failure, but the paper does not provide solutions or mitigation strategies. 2. The experimental section only presents qualitative results (such as Figures 9a and 9b) without quantitative evaluation metrics. In the field of generative models, standard metrics
The paper is well written and easy to follow, with careful explanations of the limitations of EFM (e.g. the line termination problem in Figure 2). It creatively draws from ideas in physics to propose reasonable properties of interaction fields (e.g. the start/termination of lines and flux conservation). It is especially useful that IFM provably transfers one data distribution to the other. From the visualizations in Figure 9 and the numerical results in Table 1, it seems that IFM is comparable t
The main weakness of this work is that it seems to be a repacking of the Maximum Mean Discrepancy with a field-induced kernel. Thus, I am unsure of the novelty. Given two probability distributions $p(x), q(x)$ the MMD is the squared distance between their mean embeddings in a reproducing kernel Hilbert space with some kernel $k(x,x’)$. See [1]. From my understanding, in IFM, you are replacing the kernel $k(x,x’)$ with the interaction field (so this is essentially MMD with a field-induced kernel)
- The authors provide a strong theoretical contribution by generalizing EFM and providing the most general set of requirements for the interaction field to perform data transfer. - The paper is very clearly written, intuitive, and easy to understand - The proposed IFM solves several problems with EFM and achieves better performance on several tasks. - The proposed IFM is even competitive with/outperforms diffusion/flow-matching methods. - Overall, the paper has both very strong theoretical resu
- This is somewhat of a minor point, but the authors only provide experiments on relatively "toy" problems. It would be more convincing if the authors included additional experiments on other, more challenging image generation tasks. - The paper could use some additional discussion on diffusion/flow matching to situate the work in the broader context of generative modeling
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