# Geometry-Aware Time Reparameterization for Flow-Map Distillation

arXiv: https://arxiv.org/abs/2610.02427 · HTML: https://mlsanity.com/paper/2610.02427/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 44 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [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)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Flow map matching with stochastic interpolants: A mathematical framework for consistency models](https://mlsanity.com/paper/2406.07507/) (2024)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Align Your Steps: Optimizing Sampling Schedules in Diffusion Models](https://mlsanity.com/paper/2404.14507/) (2024)
- [Minimizing Trajectory Curvature of ODE-based Generative Models](https://mlsanity.com/paper/2301.12003/) (2023)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [Flow Map Language Models: One-step Language Modeling via Continuous Denoising](https://mlsanity.com/paper/2602.16813/) (2026)
- [On the Trajectory Regularity of ODE-based Diffusion Sampling](https://mlsanity.com/paper/2405.11326/) (2024)
- [Lipschitz-Guided Design of Interpolation Schedules in Generative Models](https://mlsanity.com/paper/2509.01629/) (2025)
- [Entropic Time Schedulers for Generative Diffusion Models](https://mlsanity.com/paper/2504.13612/) (2025)
- [Optimal Scheduling of Dynamic Transport](https://mlsanity.com/paper/2504.14425/) (2025)
- [Parallel Decoding Distillation for Fast Image and Video Generation](https://mlsanity.com/paper/2607.26004/) (2026)

## Abstract (arXiv)

Flow-map distillation enables one- and few-step generation by learning finite-time transitions of a pretrained generative ODE. We investigate whether changing the teacher's time parameterization can make these transitions easier to learn. Motivated by the hypothesis that trajectory segments with large normal acceleration are harder to distill, we propose a geometry-aware time reparameterization that allocates more student time to these regions while preserving the teacher's geometric paths and terminal distribution. We derive a shared clock that equalizes a population normal-acceleration statistic under suitable assumptions, and construct a practical approximation from robust, regularized estimates across teacher trajectories. We incorporate this clock into Lagrangian flow-map distillation, using the transformed time coordinate to condition the student. The clock is estimated once before distillation and requires neither teacher retraining nor additional student parameters or inference-time network evaluations. Experiments on synthetic data, CIFAR-10, and CelebA-64 show improved sample quality over identity-time distillation at matched inference budgets, including improvements in one- and two-step image generation. The gains in one-step generation, where no intermediate sampling times can be adjusted, highlight the benefits of time reparameterization during distillation.