# Analytical Correction for Subsampling Bias in Drifting Models

arXiv: https://arxiv.org/abs/2604.27239 · HTML: https://mlsanity.com/paper/2604.27239/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Linear Complexity Randomized Self-attention Mechanism](https://mlsanity.com/paper/2204.04667/) (2022)
- [Sinkhorn-Drifting Generative Models](https://mlsanity.com/paper/2603.12366/) (2026)
- [Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences](https://mlsanity.com/paper/2603.10592/) (2026)
- [Drifting Fields are not Conservative](https://mlsanity.com/paper/2604.06333/) (2026)
- [BR-SNIS: Bias Reduced Self-Normalized Importance Sampling](https://mlsanity.com/paper/2207.06364/) (2022)
- [A Unified View of Score-Based and Drifting Models](https://mlsanity.com/paper/2603.07514/) (2026)
- [MRI-to-CT synthesis using drifting models](https://mlsanity.com/paper/2603.28498/) (2026)
- [Receding-Horizon Control via Drifting Models](https://mlsanity.com/paper/2604.04528/) (2026)

## Built on by (most cited first, 1 of 1)

- [Second Order Drifting Models](https://mlsanity.com/paper/2608.07924/) (2026)

## Abstract (arXiv)

Drifting models are capable one-step generative models trained to follow a drifting field. The field combines attractive and repulsive softmax-weighted centroids over the data and current-generator distributions. In practice, only a minibatch of n samples from each distribution is available, and each centroid is approximated by an empirical estimate. In this paper, we begin by showing that the minibatch centroid is in general a biased estimator of the target centroid, with a pointwise O(1/n) bias arising from softmax self-normalization. Correcting this bias requires the expectation over the full distribution, which is intractable. We instead approximate the leading bias term from in-batch statistics and propose Analytical Bias Correction (ABC), a closed-form plug-in adjustment. We prove that ABC reduces the bias from O(1/n) to O(1/n2), introduces no first-order increase in total variance, and preserves convex-hull containment of the corrected centroid. In practice, ABC requires only two additional lines of code and has negligible wall-time overhead under compiled execution. Toy experiments confirm the theoretical O(1/n) and O(1/n2) scaling. On CIFAR-10, ABC reduces FID and trains faster, with the largest gains at small n, where the bias is most significant.