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arXiv 2408.08307cs.LGcs.CV
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你的流形隐藏着什么秘密?理解生成模型的局部几何

What Secrets Do Your Manifolds Hold? Understanding the Local Geometry of Generative Models

Google Research(谷歌研究院);Rice University(莱斯大学);McGill University(麦吉尔大学);Google Deepmind(谷歌DeepMind)

Ahmed Imtiaz Humayun, Ibtihel Amara, Cristina Vasconcelos, Deepak Ramachandran, Candice Schumann, Junfeng He, Katherine Heller, Golnoosh Farnadi, Negar Rostamzadeh, Mohammad Havaei

AI总结:

本文通过缩放、秩和复杂度三个局部几何描述符刻画深度生成模型流形,揭示其与生成美学、多样性及记忆化的关系,并提出基于几何奖励的引导方法以自提升Stable Diffusion的生成质量。

摘要:

深度生成模型经常被用来利用有限数量的样本学习复杂数据分布的连续表示。对于任何生成模型,包括具有扩散或Transformer架构的预训练基础模型,生成性能在学习到的数据流形上可能存在显著差异。在本文中,我们研究学习到的流形的局部几何及其与各种生成模型生成结果的关系,这些模型包括DDPM、扩散Transformer(DiT)和Stable Diffusion 1.4。基于连续分段线性(CPWL)生成器理论,我们用三个几何描述符来刻画局部几何——缩放(ψ)、秩(ν)和复杂度/非平滑性(δ)。我们提供定量和定性证据表明,对于给定的潜在-图像对,局部描述符能够指示生成模型的美学质量、多样性和记忆化程度。最后,我们证明通过为Stable Diffusion训练一个关于局部缩放的奖励模型,我们可以在去噪过程中利用基于“几何奖励”的引导来自我提升生成美学质量和多样性。

英文摘要:

Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer architectures, generation performance can significantly vary across the learned data manifold. In this paper we study the local geometry of the learned manifold and its relationship to generation outcomes for a wide range of generative models, including DDPM, Diffusion Transformer (DiT), and Stable Diffusion 1.4. Building on the theory of continuous piecewise-linear (CPWL) generators, we characterize the local geometry in terms of three geometric descriptors - scaling ($ψ$), rank ($ν$), and complexity/un-smoothness ($δ$). We provide quantitative and qualitative evidence showing that for a given latent-image pair, the local descriptors are indicative of generation aesthetics, diversity, and memorization by the generative model. Finally, we demonstrate that by training a reward model on the local scaling for Stable Diffusion, we can self-improve both generation aesthetics and diversity using `geometry reward' based guidance during denoising.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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