# GeoSPRINT: Geometric Redundancy-Aware Step Pruning for Inference in Diffusion Trajectories

arXiv: https://arxiv.org/abs/2609.02160 · HTML: https://mlsanity.com/paper/2609.02160/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 18 of its 20 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 18 of 18)

- [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)
- [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)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [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)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [On Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.00132/) (2021)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow](https://mlsanity.com/paper/2410.07303/) (2024)
- [Adaptive Non-uniform Timestep Sampling for Accelerating Diffusion Model Training](https://mlsanity.com/paper/2411.09998/) (2024)
- [Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timesteps](https://mlsanity.com/paper/2602.12624/) (2026)

## Abstract (arXiv)

Diffusion models achieve high sample quality but remain expensive at inference time because sampling requires many sequential neural function evaluations (NFEs). Existing acceleration methods either use fixed step-skipping schedules, adapt step sizes based on local numerical error, or require additional training. We introduce GeoSPRINT (Geometric Step Pruning for Inference in Trajectories), a training-free framework for constructing non-uniform sampling schedules from the geometry of denoising trajectories. GeoSPRINT detects geometrically redundant steps using a hyperplanarity test in latent space, implemented efficiently via QR factorization, and converts the resulting redundancy profile into a sampling schedule that allocates more steps to high-curvature regions of the trajectory. In addition, we introduce the trajectory projection score αtraj, a residual-variance metric that quantifies trajectory straightness and serves as a model-free diagnostic for rectified flow quality. Across CIFAR-10 (32×32), LSUN Church (256×256), and Stable Diffusion v1.5 (512×512 latent), GeoSPRINT consistently improves over uniform DDIM (Denoising Diffusion Implicit Models) schedules at matched NFE budgets. On CIFAR-10, GeoSPRINT improves FID (Fr'echet Inception Distance) by 0.7-1.1 over DDIM across 49-89 NFEs and surpasses DPM-Solver++ at NFE≥30 despite using a first-order DDIM solver. On LSUN Church, it reduces FID from 1.48 to 1.26 at 52 steps, and on Stable Diffusion v1.5 it achieves up to 1.93 FID improvement over DDIM. These results show that trajectory geometry provides a useful global signal for allocating inference steps and that schedule quality can substantially improve diffusion sampling efficiency without retraining.