# Condition-Wise Sinkhorn Drifting for One-Shot Learned Channel Simulation

arXiv: https://arxiv.org/abs/2606.17893 · HTML: https://mlsanity.com/paper/2606.17893/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion for compression and wireless, one of 14 directions in Diffusion models.
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Placed in

- Diffusion models / [Diffusion for compression and wireless](https://mlsanity.com/diffusion/diffusion-for-compression-and-wireless/)

## Builds on (most cited first, 13 of 13)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Generative Diffusion Models for High Dimensional Channel Estimation](https://mlsanity.com/paper/2408.10501/) (2024)
- [Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation](https://mlsanity.com/paper/2403.03545/) (2024)
- [One-Step Generative Modeling via Wasserstein Gradient Flows](https://mlsanity.com/paper/2605.11755/) (2026)
- [Generating High Dimensional User-Specific Wireless Channels using Diffusion Models](https://mlsanity.com/paper/2409.03924/) (2024)
- [Joint channel estimation and data detection in massive MIMO systems based on diffusion models](https://mlsanity.com/paper/2311.10311/) (2023)
- [The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning](https://mlsanity.com/paper/2602.18428/) (2026)
- [Diffusion Models for Accurate Channel Distribution Generation](https://mlsanity.com/paper/2309.10505/) (2023)

## Abstract (arXiv)

Learned communication systems may evaluate stochastic channel surrogates millions of times inside differentiable training loops, making diffusion-style reverse sampling expensive. This paper proposes condition-wise Sinkhorn drifting, a one-shot channel surrogate that preserves the transmitted symbol and transports only the conditional output laws (p(ymid x)). We formulate a conditional Sinkhorn objective over repeated outputs at the same transmitted symbol and train the generator with finite-sample barycentric velocities followed by detached particle regression. Experiments on additive white Gaussian noise (AWGN), Rayleigh fading, solid-state power amplifier (SSPA) nonlinearity, and a compact tapped-delay-line (TDL) channel compare direct drifting, joint Sinkhorn drifting, condition-wise Sinkhorn drifting, conditional denoising diffusion probabilistic modeling (DDPM), denoising diffusion implicit modeling (DDIM), and Wasserstein generative adversarial network (WGAN) references. Within the evaluated one-shot drifting-family variants, condition-wise Sinkhorn is strongest under conditional diagnostics and symbolic-coding checks, while diffusion remains strongest on the hardest downstream symbol-error-rate (SER) curves. The resulting operating point is a condition-preserving one-shot simulator for settings where repeated channel calls make diffusion-style sampling too costly.