Transformers converge globally to the optimal DDPM denoiser for multi-token GMMs via self-attention mean denoising, with explicit token and iteration requirements.
arXiv preprint arXiv:2501.12982 , year=
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For Gaussian mixture targets, diffusion discretization error and step complexity are controlled by latent entropy rather than ambient dimension.
For a broad class of coefficients, diffusion models achieve Õ(k/ε) iteration complexity for ε-accurate TV sampling under low-dimensional structure, independent of ambient dimension.
Reusing source latent spaces in diffusion models under distribution shift produces target score error set by principal-angle misalignment and diffusion-time-amplified ambient noise.
Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.
citing papers explorer
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Transformers Learn the Optimal DDPM Denoiser for Multi-Token GMMs
Transformers converge globally to the optimal DDPM denoiser for multi-token GMMs via self-attention mean denoising, with explicit token and iteration requirements.
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When Diffusion Model Can Ignore Dimension: An Entropy-Based Theory
For Gaussian mixture targets, diffusion discretization error and step complexity are controlled by latent entropy rather than ambient dimension.
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Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices
For a broad class of coefficients, diffusion models achieve Õ(k/ε) iteration complexity for ε-accurate TV sampling under low-dimensional structure, independent of ambient dimension.
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On the Limits of Latent Reuse in Diffusion Models
Reusing source latent spaces in diffusion models under distribution shift produces target score error set by principal-angle misalignment and diffusion-time-amplified ambient noise.
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On the Robustness of Distribution Support under Diffusion Guidance
Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.