Overclocking Electrostatic Generative Models

Electrostatic generative models such as PFGM++ have recently emerged as a powerful framework, achieving competitive performance in image synthesis. PFGM++ operates in an extended data space with auxiliary dimensionality $D$, recovering the diffusion model framework as $D\to\infty$, while yielding superior empirical results for finite $D$. Like diffusion models, PFGM++ relies on expensive ODE simulations to generate samples, making it computationally costly. To address this, we propose Inverse Poisson Flow Matching (IPFM), a principled distillation framework that accelerates electrostatic generative models across all values of $D$. Our IPFM reformulates distillation as an inverse problem: learning a generator whose induced electrostatic field matches that of the teacher. We derive a tractable training objective for this problem and show that, as $D\to\infty$, our IPFM closely recovers Score Identity Distillation (SiD), a recent method for distilling diffusion models. Empirically, our IPFM produces distilled generators that achieve near-teacher or even superior sample quality using only a few function evaluations. Moreover, we find that one-step generator distillation converges faster at finite $D$ than in the $D\to\infty$ diffusion limit, aligning with prior evidence that finite-$D$ PFGM++ models offer more favorable optimization and sampling behavior.

Modern image-generation systems, such as diffusion models, can produce high-quality images but often require many computational steps to generate each sample. This makes them slow and expensive to use. This paper studies a newer family of physics-inspired generative models, called electrostatic generative models, which generate data by using ideas similar to electric fields. Although these models can achieve strong image quality, they also usually require costly simulations during sampling. We introduce Inverse Poisson Flow Matching (IPFM), a method for making these electrostatic generative models much faster. Instead of running the original model through many simulation steps, IPFM trains a smaller generator to imitate the behavior of the original model’s electrostatic field. This allows the model to generate images in only one or a few steps while keeping similar, and sometimes better, image quality. Our experiments show that IPFM can significantly reduce sampling cost on standard image-generation benchmarks. The results also suggest that finite-dimensional electrostatic models may be easier to distill than standard diffusion models, making them a promising direction for efficient generative modeling.