# Variational Trajectory Optimization of Anisotropic Diffusion Schedules

arXiv: https://arxiv.org/abs/2602.19512 · HTML: https://mlsanity.com/paper/2602.19512/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## 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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [VideoFusion: Decomposed Diffusion Models for High-Quality Video Generation](https://mlsanity.com/paper/2303.08320/) (2023)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models](https://mlsanity.com/paper/2305.10474/) (2023)
- [Subspace Diffusion Generative Models](https://mlsanity.com/paper/2205.01490/) (2022)
- [Diffusion Models With Learned Adaptive Noise](https://mlsanity.com/paper/2312.13236/) (2023)
- [How I Warped Your Noise: a Temporally-Correlated Noise Prior for Diffusion Models](https://mlsanity.com/paper/2504.03072/) (2025)
- [Blue noise for diffusion models](https://mlsanity.com/paper/2402.04930/) (2024)
- [Edge-preserving noise for diffusion models](https://mlsanity.com/paper/2410.01540/) (2024)

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

- [Learning When to Denoise: Optimizing Asynchronous Schedules for Latent Diffusion](https://mlsanity.com/paper/2606.19662/) (2026)

## Abstract (arXiv)

We introduce a variational framework for diffusion models with anisotropic noise schedules parameterized by a matrix-valued path Mt(θ) that allocates noise across subspaces. Central to our framework is a trajectory-level objective that jointly trains the score network and learns Mt(θ), which encompasses general parameterization classes of matrix-valued noise schedules. We further derive an estimator for the derivative with respect to θ of the score that enables efficient optimization of the Mt(θ) schedule. For inference, we develop an efficiently-implementable reverse-ODE solver that is an anisotropic generalization of the second-order Heun discretization algorithm. Across CIFAR-10, AFHQv2, FFHQ, and ImageNet-64, our method consistently improves upon the baseline EDM model in all NFE regimes. Code is available at https://github.com/lizeyu090312/anisotropic-diffusion-paper.