# Efficient Score Pre-computation for Diffusion Models via Cross-Matrix Krylov Projection

arXiv: https://arxiv.org/abs/2511.17634 · HTML: https://mlsanity.com/paper/2511.17634/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Placed in

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

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Efficient Learning of Generative Models via Finite-Difference Score Matching](https://mlsanity.com/paper/2007.03317/) (2020)
- [Probability flow solution of the Fokker-Planck equation](https://mlsanity.com/paper/2206.04642/) (2022)
- [Efficient Denoising using Score Embedding in Score-based Diffusion Models](https://mlsanity.com/paper/2404.06661/) (2024)

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

- [PhyloSDF: Phylogenetically-Conditioned Neural Generation of 3D Skull Morphology via Residual Flow Matching](https://mlsanity.com/paper/2604.25371/) (2026)

## Abstract (arXiv)

This paper presents a novel framework to accelerate score-based diffusion models. It first converts the standard stable diffusion model into the Fokker-Planck formulation which results in solving large linear systems for each image. For training involving many images, it can lead to a high computational cost. The core innovation is a cross-matrix Krylov projection method that exploits mathematical similarities between matrices, using a shared subspace built from ``seed" matrices to rapidly solve for subsequent ``target" matrices. Our experiments show that this technique achieves a 15.8% to 43.7% time reduction over standard sparse solvers. Additionally, we compare our method against DDPM baselines in denoising tasks, showing a speedup of up to 115×. Furthermore, under a fixed computational budget, our model is able to produce high-quality images while DDPM fails to generate recognizable content, illustrating our approach is a practical method for efficient generation in resource-limited settings.