# A Prior of a Googol Gaussians: a Tensor Ring Induced Prior for Generative Models

arXiv: https://arxiv.org/abs/1910.13148 · HTML: https://mlsanity.com/paper/1910.13148/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Cauchy-Schwarz Regularized Autoencoder](https://mlsanity.com/paper/2101.02149/) (2021)
- [Privacy-preserving machine learning with tensor networks](https://mlsanity.com/paper/2202.12319/) (2022)
- [tntorch: Tensor Network Learning with PyTorch](https://mlsanity.com/paper/2206.11128/) (2022)
- [Cluster-guided Image Synthesis with Unconditional Models](https://mlsanity.com/paper/2112.12911/) (2021)
- [Spider GAN: Leveraging Friendly Neighbors to Accelerate GAN Training](https://mlsanity.com/paper/2305.07613/) (2023)
- [Scalable Bayesian Tensor Ring Factorization for Multiway Data Analysis](https://mlsanity.com/paper/2412.03321/) (2024)
- [Tensor-Train Point Cloud Compression and Efficient Approximate Nearest-Neighbor Search](https://mlsanity.com/paper/2410.04462/) (2024)
- [Score-Based Model for Low-Rank Tensor Recovery](https://mlsanity.com/paper/2506.22295/) (2025)

## Abstract (arXiv)

Generative models produce realistic objects in many domains, including text, image, video, and audio synthesis. Most popular models---Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs)---usually employ a standard Gaussian distribution as a prior. Previous works show that the richer family of prior distributions may help to avoid the mode collapse problem in GANs and to improve the evidence lower bound in VAEs. We propose a new family of prior distributions---Tensor Ring Induced Prior (TRIP)---that packs an exponential number of Gaussians into a high-dimensional lattice with a relatively small number of parameters. We show that these priors improve Fr'echet Inception Distance for GANs and Evidence Lower Bound for VAEs. We also study generative models with TRIP in the conditional generation setup with missing conditions. Altogether, we propose a novel plug-and-play framework for generative models that can be utilized in any GAN and VAE-like architectures.