# A Unified View of Score-Based and Drifting Models

arXiv: https://arxiv.org/abs/2603.07514 · HTML: https://mlsanity.com/paper/2603.07514/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [The Principles of Diffusion Models](https://mlsanity.com/paper/2510.21890/) (2025)
- [Adversarial Distribution Matching for Diffusion Distillation Towards Efficient Image and Video Synthesis](https://mlsanity.com/paper/2507.18569/) (2025)
- [Coulomb GANs: Provably Optimal Nash Equilibria via Potential Fields](https://mlsanity.com/paper/1708.08819/) (2017)
- [Idempotent Generative Network](https://mlsanity.com/paper/2311.01462/) (2023)
- [CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models](https://mlsanity.com/paper/2509.24526/) (2025)
- [A Long-Short Flow-Map Perspective for Drifting Models](https://mlsanity.com/paper/2602.20463/) (2026)
- [The Score-Difference Flow for Implicit Generative Modeling](https://mlsanity.com/paper/2304.12906/) (2023)

## Built on by (most cited first, 11 of 11)

- [Drifting Fields are not Conservative](https://mlsanity.com/paper/2604.06333/) (2026)
- [Drifting Field Policy: A One-Step Generative Policy via Wasserstein Gradient Flow](https://mlsanity.com/paper/2605.07727/) (2026)
- [Analytical Correction for Subsampling Bias in Drifting Models](https://mlsanity.com/paper/2604.27239/) (2026)
- [Lookahead Drifting Model](https://mlsanity.com/paper/2605.04060/) (2026)
- [Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence](https://mlsanity.com/paper/2606.19876/) (2026)
- [Unifying Distributional Training for One-Step Visual Generation](https://mlsanity.com/paper/2609.35763/) (2026)
- [Identifiability and Stability of Generative Drifting in the Companion-Elliptic Kernel Family](https://mlsanity.com/paper/2604.24196/) (2026)
- [Generative Modeling with Flux Matching](https://mlsanity.com/paper/2605.07319/) (2026)
- [Finite-Probe Total-Variation Certificates for Finite-Basis Drifting Models](https://mlsanity.com/paper/2608.01547/) (2026)
- [One-Step Generation via Riemannian Wasserstein Gradient Flows](https://mlsanity.com/paper/2610.04454/) (2026)
- [Learning Discriminative Geometry for Drifting Models](https://mlsanity.com/paper/2610.04703/) (2026)

## Abstract (arXiv)

Drifting models train one-step generators by optimizing a kernel-induced mean-shift discrepancy between the data and model distributions, with Laplace kernels used by default in practice. At each point, this discrepancy compares the kernel-weighted displacement toward nearby data samples with the corresponding displacement toward nearby model samples, thereby defining a transport direction for generated samples. In this paper, we show that drifting is more closely connected to score-based generative modeling than it may first appear, establishing a precise link to the score-matching principle underlying diffusion models. For Gaussian kernels, the population mean-shift field exactly equals the difference between the scores (i.e., the gradient-log-densities) of the Gaussian-smoothed data and model distributions. This identity follows from Tweedie's formula, which links the score of a Gaussian-smoothed density to its conditional mean, and implies that Gaussian-kernel drifting is exactly a score-matching objective on smoothed distributions. More generally, we derive an exact decomposition for radial kernels in which mean shift equals a score-based field plus a residual term. For the practical Laplace kernel, we further show theoretically and empirically that this residual is negligible in high dimension, implying that the transport field used in practice is nearly score-based. Our results reveal a structural connection to diffusion models: both methods use score-mismatch transport directions, but drifting realizes the score nonparametrically through kernel-based estimates, whereas diffusion models learn it parametrically with neural networks.