# Antithetic Noise in Diffusion Models

arXiv: https://arxiv.org/abs/2506.06185 · HTML: https://mlsanity.com/paper/2506.06185/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 40 of its 63 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Placed in

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

## Builds on (most cited first, 30 of 40)

- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [CADS: Unleashing the Diversity of Diffusion Models through Condition-Annealed Sampling](https://mlsanity.com/paper/2310.17347/) (2023)
- [InitNO: Boosting Text-to-Image Diffusion Models via Initial Noise Optimization](https://mlsanity.com/paper/2404.04650/) (2024)
- [Golden Noise for Diffusion Models: A Learning Framework](https://mlsanity.com/paper/2411.09502/) (2024)
- [Not All Noises Are Created Equally:Diffusion Noise Selection and Optimization](https://mlsanity.com/paper/2407.14041/) (2024)
- [Deep Lattice Networks and Partial Monotonic Functions](https://mlsanity.com/paper/1709.06680/) (2017)
- [CONFORM: Contrast is All You Need For High-Fidelity Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.06059/) (2023)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [Understanding Generalizability of Diffusion Models Requires Rethinking the Hidden Gaussian Structure](https://mlsanity.com/paper/2410.24060/) (2024)
- [Exploiting the Signal-Leak Bias in Diffusion Models](https://mlsanity.com/paper/2309.15842/) (2023)

## Built on by (most cited first, 4 of 4)

- [Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performance](https://mlsanity.com/paper/2601.22443/) (2026)
- [Couple to Control: Joint Initial Noise Design in Diffusion Models](https://mlsanity.com/paper/2605.11311/) (2026)
- [DiFA: Inference-Time Forward-Process Alignment for Diffusion Models](https://mlsanity.com/paper/2607.17972/) (2026)
- [DiffImaginE: Imagine to Verify Entity Types with Diffusion](https://mlsanity.com/paper/2608.03025/) (2026)

## Abstract (arXiv)

We systematically study antithetic initial noise in diffusion models, discovering that pairing each noise sample with its negation consistently produces strong negative correlation. This universal phenomenon holds across datasets, model architectures, conditional and unconditional sampling, and even other generative models such as VAEs and Normalizing Flows. To explain it, we combine experiments and theory and propose a textitsymmetry conjecture that the learned score function is approximately affine antisymmetric (odd symmetry up to a constant shift), supported by empirical evidence. This negative correlation leads to substantially more reliable uncertainty quantification with up to 90% narrower confidence intervals. We demonstrate these gains on tasks including estimating pixel-wise statistics and evaluating diffusion inverse solvers. We also provide extensions with randomized quasi-Monte Carlo noise designs for uncertainty quantification, and explore additional applications of the antithetic noise design to improve image editing and generation diversity. Our framework is training-free, model-agnostic, and adds no runtime overhead. Code is available at https://github.com/jjia131/Antithetic-Noise-in-Diffusion-Models-page.