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[2602.16498] Fast and Scalable Analytical Diffusion
Summary
The paper presents GoldDiff, a novel framework for analytical diffusion that enhances scalability and speed in generative modeling by dynamically identifying relevant data subsets.
Why It Matters
As generative models become increasingly complex, the need for efficient algorithms that can handle large datasets without sacrificing performance is critical. GoldDiff addresses scalability issues in analytical diffusion, potentially transforming practices in machine learning and AI applications.
Key Takeaways
- GoldDiff offers a training-free framework that improves inference speed by 71 times on AFHQ datasets.
- The method identifies a 'Golden Subset' of data, reducing the need for full dataset scans.
- Theoretical guarantees ensure that the sparse approximation converges to the exact score, enhancing reliability.
Computer Science > Machine Learning arXiv:2602.16498 (cs) [Submitted on 18 Feb 2026] Title:Fast and Scalable Analytical Diffusion Authors:Xinyi Shang, Peng Sun, Jingyu Lin, Zhiqiang Shen View a PDF of the paper titled Fast and Scalable Analytical Diffusion, by Xinyi Shang and 3 other authors View PDF HTML (experimental) Abstract:Analytical diffusion models offer a mathematically transparent path to generative modeling by formulating the denoising score as an empirical-Bayes posterior mean. However, this interpretability comes at a prohibitive cost: the standard formulation necessitates a full-dataset scan at every timestep, scaling linearly with dataset size. In this work, we present the first systematic study addressing this scalability bottleneck. We challenge the prevailing assumption that the entire training data is necessary, uncovering the phenomenon of Posterior Progressive Concentration: the effective golden support of the denoising score is not static but shrinks asymptotically from the global manifold to a local neighborhood as the signal-to-noise ratio increases. Capitalizing on this, we propose Dynamic Time-Aware Golden Subset Diffusion (GoldDiff), a training-free framework that decouples inference complexity from dataset size. Instead of static retrieval, GoldDiff uses a coarse-to-fine mechanism to dynamically pinpoint the ''Golden Subset'' for inference. Theoretically, we derive rigorous bounds guaranteeing that our sparse approximation converges to the exact...
