Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
Support points summarize a large dataset through a smaller set of representative points that can be used for data operations, such as Monte Carlo integration, without requiring access to the full dataset. In this sense, support points offer a compact yet informative representation of the original data. We build on this idea to introduce a generative modeling framework based on random weighted support points, where the randomness arises from a weighting scheme inspired by the Dirichlet process and the Bayesian bootstrap. The proposed method generates diverse and interpretable sample sets from a fixed dataset, without relying on probabilistic modeling assumptions or neural network architectures. We present the theoretical formulation of the method and develop an efficient optimization algorithm based on the Convex--Concave Procedure (CCP). Empirical results on the MNIST and CelebA-HQ datasets show that our approach produces high-quality and diverse outputs at a fraction of the computational cost of black-box alternatives such as Generative Adversarial Networks (GANs) or Denoising Diffusion Probabilistic Models (DDPMs). These results suggest that random weighted support points offer a principled, scalable, and interpretable alternative for generative modeling. A key feature is their ability to produce genuinely interpolative samples that preserve underlying data structure.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 20 of its 32 references that are in the map. First posted on arXiv 28 Aug 2025.
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20 of 32 references.
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- 2024Denoising Diffusion Probabilistic Models in Six Simple Steps6 Feb
- 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
- 2021Diffusion Models Beat GANs on Image Synthesis11 May
- 2021Improved Denoising Diffusion Probabilistic Models18 Feb
- 2020Denoising Diffusion Implicit Models6 Oct
- 2020Denoising Diffusion Probabilistic Models19 Jun
Other references · 14
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- 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,588
- 2016Improved Techniques for Training GANscited by 2,970
- 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,626
- 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,054
- 2019An Introduction to Variational Autoencoderscited by 1,000
- 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 464
- 2016NIPS 2016 Tutorial: Generative Adversarial Networkscited by 285
- 2018Stein Pointscited by 43
2 more
- 2016Support pointscited by 39
- 2017Projected support points: a new method for high-dimensional data reductioncited by 3
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