# Sinkhorn-Drifting Generative Models

arXiv: https://arxiv.org/abs/2603.12366 · HTML: https://mlsanity.com/paper/2603.12366/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 10 of 10)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Adversarial Latent Autoencoders](https://mlsanity.com/paper/2004.04467/) (2020)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Entropic estimation of optimal transport maps](https://mlsanity.com/paper/2109.12004/) (2021)
- [Coulomb GANs: Provably Optimal Nash Equilibria via Potential Fields](https://mlsanity.com/paper/1708.08819/) (2017)
- [Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport](https://mlsanity.com/paper/1711.01851/) (2017)

## Built on by (most cited first, 24 of 24)

- [One-Step Generative Modeling via Wasserstein Gradient Flows](https://mlsanity.com/paper/2605.11755/) (2026)
- [Drifting Fields are not Conservative](https://mlsanity.com/paper/2604.06333/) (2026)
- [On the Wasserstein Gradient Flow Interpretation of Drifting Models](https://mlsanity.com/paper/2605.05118/) (2026)
- [Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Models](https://mlsanity.com/paper/2605.22795/) (2026)
- [Three-Body Scattering for Generative Modeling](https://mlsanity.com/paper/2607.18198/) (2026)
- [Friction-Augmented Drifting Models for Resource-Efficient Domain Translation](https://mlsanity.com/paper/2604.18194/) (2026)
- [Teacher-Feature Drifting: One-Step Diffusion Distillation with Pretrained Diffusion Representations](https://mlsanity.com/paper/2605.07327/) (2026)
- [Drifting Field Policy: A One-Step Generative Policy via Wasserstein Gradient Flow](https://mlsanity.com/paper/2605.07727/) (2026)
- [Amortized Optimal Transport from Sliced Potentials](https://mlsanity.com/paper/2604.15114/) (2026)
- [Sliced-Regularized Optimal Transport](https://mlsanity.com/paper/2604.23944/) (2026)
- [Drift Flow Matching](https://mlsanity.com/paper/2605.17244/) (2026)
- [Analytical Correction for Subsampling Bias in Drifting Models](https://mlsanity.com/paper/2604.27239/) (2026)
- [Second Order Drifting Models](https://mlsanity.com/paper/2608.07924/) (2026)
- [Identifiability and Stability of Generative Drifting in the Companion-Elliptic Kernel Family](https://mlsanity.com/paper/2604.24196/) (2026)
- [SymDrift: One-Shot Generative Modeling under Symmetries](https://mlsanity.com/paper/2605.06140/) (2026)
- [Drifting Models for Surrogate Flow Modeling](https://mlsanity.com/paper/2606.07481/) (2026)
- [DriftST: One-Step Generative Inference of Spatial Transcriptomics from H&E Histology](https://mlsanity.com/paper/2607.04740/) (2026)
- [Finite-Probe Total-Variation Certificates for Finite-Basis Drifting Models](https://mlsanity.com/paper/2608.01547/) (2026)
- [One-Step Generative Modeling via Unbalanced Optimal Transport](https://mlsanity.com/paper/2609.32708/) (2026)
- [Sliced Orlicz-Wasserstein](https://mlsanity.com/paper/2609.32847/) (2026)
- [One-Step Generative Modeling via Training Dynamics Action](https://mlsanity.com/paper/2610.00518/) (2026)
- [One-Step Generation via Riemannian Wasserstein Gradient Flows](https://mlsanity.com/paper/2610.04454/) (2026)
- [Amortised Inference through One-Step Implicit Sampling](https://mlsanity.com/paper/2610.12679/) (2026)
- [Drift, Then Spread: Learning One-Step Generative Policies for Online Reinforcement Learning](https://mlsanity.com/paper/2610.15662/) (2026)

## Abstract (arXiv)

We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an attractive term toward the target distribution and a repulsive/self-correction term toward the current model, both expressed via one-sided normalized Gibbs kernels. We show that Sinkhorn divergence yields an analogous cross-minus-self structure, but with each term defined by entropic optimal-transport couplings obtained through two-sided Sinkhorn scaling (i.e., enforcing both marginals). This provides a precise sense in which drifting acts as a surrogate for a Sinkhorn-divergence gradient flow, interpolating between one-sided normalization and full two-sided Sinkhorn scaling. Crucially, this connection resolves an identifiability gap in prior drifting formulations: leveraging the definiteness of the Sinkhorn divergence, we show that zero drift (equilibrium of the dynamics) implies that the model and target measures match. Experiments show that Sinkhorn drifting reduces sensitivity to kernel temperature and improves one-step generative quality, trading off additional training time for a more stable optimization, without altering the inference procedure used by drift methods. These theoretical gains translate to strong low-temperature improvements in practice: on FFHQ-ALAE at the lowest temperature setting we evaluate, Sinkhorn drifting reduces mean FID from 187.7 to 37.1 and mean latent EMD from 453.3 to 144.4, while on MNIST it preserves full class coverage across the temperature sweep. Project page: https://mint-vu.github.io/SinkhornDrifting/