Antithetic Noise in Diffusion Models
Jing Jia, Sifan Liu, Bowen Song, Wei Yuan, Liyue Shen, Guanyang Wang
TL;DR
This paper introduces a universal antithetic noise technique in diffusion models that improves uncertainty quantification and is applicable across various generative models without additional training or runtime costs.
Contribution
It uncovers the negative correlation phenomenon in diffusion models' noise, proposes a symmetry conjecture for the learned score function, and demonstrates practical benefits for uncertainty estimation and image generation.
Findings
Up to 90% narrower confidence intervals in uncertainty quantification.
Universal negative correlation observed across datasets and models.
Enhanced image editing and diversity through antithetic noise design.
Abstract
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 \textit{symmetry 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 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…
Peer Reviews
Decision·ICLR 2026 Poster
(i) The paper proposes a simple, training-free, model-agnostic procedure with no runtime overhead (ii) The paper features broad empirical validation across datasets, samplers (DDIM/DDPM), architectures, and even VAEs/flows (iii) Antithetic Monte Carlo is well motivated and yields substantial, measurable variance reduction (iv) Beyond the main paper, the work provides good reproducibility details and extensive appendices
(i) While theoretical support for the symmetry conjecture is partial and focused on high-noise regimes, the symmetry conjecture remains unproven in generality. The novelty lies mostly in documenting the phenomenon antithetic variance reduction and its strength in diffusion models. (ii) Many results use pixel-level correlations and simple statistics, while semantic-level uncertainty and quality metrics (e.g., FID, CLIP alignment) are less explored or could be expanded upon more. (iii) Condition
1. The study of antithetical initial noise in diffusion models appears new to me. 2. Although the empirical results are not perfectly aligned with the theoretical argument in Lemma 1, the characterization is interesting and could inspire future studies. 3. The paper is well-written and easy to follow.
1. The work would be more complete if the authors could provide some discussion on why the score function admits this affine antisymmetric property. 2. While the work shows that the found fact could result in new methods to do uncertain quantification with significantly narrower CI, as we deal with the generative models, we can potentially generate an infinite number of samples, which potentially drops the significance of the proposed methods. 3. I am a bit confused about the results in Table 1
- The paper is clearly presented and easy to follow. - The underlying principle is simple and elegant and can be implemented easily. - The conjecture is simple and relevant to the evidence presented. - The experiments are thorough and convincing in terms of the superiority of antithetic vs independent sampling for uncertainty quantification and posterior sampling.
- The novelty feels quite limited. Antithetic sampling is a well-established variance-reduction technique, and the fact that fully negatively correlated samples passed into what is essentially a flow map yield back partially negatively correlated outputs feels like expected behaviour, not really a "universal discovery". - The theoretical justification of the conjecture in the high-noise regime, although nicely presented, is fairly trivial since it mostly relies on the well-known fact that the s
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Taxonomy
TopicsGenerative Adversarial Networks and Image Synthesis · Stochastic Gradient Optimization Techniques · Markov Chains and Monte Carlo Methods
MethodsDiffusion