# Learning Discriminative Geometry for Drifting Models

arXiv: https://arxiv.org/abs/2610.04703 · HTML: https://mlsanity.com/paper/2610.04703/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 43 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Dilated Residual Networks](https://mlsanity.com/paper/1705.09914/) (2017)
- [Projected GANs Converge Faster](https://mlsanity.com/paper/2111.01007/) (2021)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [One-Step Generative Modeling via Wasserstein Gradient Flows](https://mlsanity.com/paper/2605.11755/) (2026)
- [Generative Drifting is Secretly Score Matching: a Spectral and Variational Perspective](https://mlsanity.com/paper/2603.09936/) (2026)
- [MonoFlow: Rethinking Divergence GANs via the Perspective of Wasserstein Gradient Flows](https://mlsanity.com/paper/2302.01075/) (2023)
- [A Unified View of Score-Based and Drifting Models](https://mlsanity.com/paper/2603.07514/) (2026)

## Abstract (arXiv)

Recently proposed Drifting Models shift iterative distribution refinement from inference to training, enabling effective one-step generation. However, their performance on complex image datasets depends strongly on the representation used to construct the drifting field: pixel-space drifting performs poorly, whereas pretrained feature spaces substantially improve sample quality for reasons that remain unclear. We trace this gap to the discriminative geometry of the representation, which determines sample weighting in kernel density estimation (KDE) and, consequently drift. We introduce persistent representation learning, which continuously learns a more discriminative representation geometry as the generator evolves across batches. We further establish a current-step gradient equivalence between the KDE ratio loss and drift regression loss under matched conditions, connecting density-ratio-based generator optimization to empirical drifting and motivating direct control of the drifting velocity. Across multiple datasets, our method learns effective discriminative representations directly from pixels and reduces FID by approximately 82-95% over the original pixel-space Drifting Models, without pretrained encoders. Adapting pretrained representations and applying velocity clipping provide further gains.