# Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling

arXiv: https://arxiv.org/abs/2508.21255 · HTML: https://mlsanity.com/paper/2508.21255/

## 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.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Stein Points](https://mlsanity.com/paper/1803.10161/) (2018)
- [Support points](https://mlsanity.com/paper/1609.01811/) (2016)
- [Denoising Diffusion Probabilistic Models in Six Simple Steps](https://mlsanity.com/paper/2402.04384/) (2024)
- [Projected support points: a new method for high-dimensional data reduction](https://mlsanity.com/paper/1708.06897/) (2017)

## 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.