# Generative Modeling via Kernelized Stochastic Interpolants

arXiv: https://arxiv.org/abs/2602.20070 · HTML: https://mlsanity.com/paper/2602.20070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 19 of 19)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [ZipLoRA: Any Subject in Any Style by Effectively Merging LoRAs](https://mlsanity.com/paper/2311.13600/) (2023)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [Sampling in Unit Time with Kernel Fisher-Rao Flow](https://mlsanity.com/paper/2401.03892/) (2024)
- [Diffusion Soup: Model Merging for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2406.08431/) (2024)
- [Distributional Diffusion Models with Scoring Rules](https://mlsanity.com/paper/2502.02483/) (2025)
- [Multiscale Sparse Microcanonical Models](https://mlsanity.com/paper/1801.02013/) (2018)
- [Non-Gaussian information from weak lensing data via deep learning](https://mlsanity.com/paper/1802.01212/) (2018)
- [Scattering Spectra Models for Physics](https://mlsanity.com/paper/2306.17210/) (2023)
- [Denoising Data with Measurement Error Using a Reproducing Kernel-based Diffusion Model](https://mlsanity.com/paper/2501.00212/) (2024)
- [MGD: Moment Guided Diffusion for Maximum Entropy Generation](https://mlsanity.com/paper/2602.17211/) (2026)

## Abstract (arXiv)

We develop a kernel method for generative modeling within the stochastic interpolant framework, replacing neural network training with linear systems. The drift of the generative SDE is hat bt(x) = nablaφ(x)^topηt, where ηt ∈ ℝP solves a P× P system computable from data, with P independent of the data dimension d. Since estimates are inexact, the diffusion coefficient Dt affects sample quality; the optimal Dt^* from Girsanov diverges at t=0, but this poses no difficulty and we develop an integrator that handles it seamlessly. The framework accommodates diverse feature maps: scattering transforms, pretrained generative models, etc, enabling generation and model combination without neural network training. We demonstrate the approach on financial time series, turbulence, and image generation.