# Guiding Time-Varying Generative Models with Natural Gradients on Exponential Family Manifold

arXiv: https://arxiv.org/abs/2502.07650 · HTML: https://mlsanity.com/paper/2502.07650/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 52 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 30 of 35)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Diffusion-GAN: Training GANs with Diffusion](https://mlsanity.com/paper/2206.02262/) (2022)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [NaturalSpeech: End-to-End Text to Speech Synthesis with Human-Level Quality](https://mlsanity.com/paper/2205.04421/) (2022)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem](https://mlsanity.com/paper/1802.08089/) (2018)
- [SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence](https://mlsanity.com/paper/2006.02509/) (2020)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Density Estimation in Infinite Dimensional Exponential Families](https://mlsanity.com/paper/1312.3516/) (2013)
- [Deep Generative Learning via Variational Gradient Flow](https://mlsanity.com/paper/1901.08469/) (2019)
- [Sampling in Unit Time with Kernel Fisher-Rao Flow](https://mlsanity.com/paper/2401.03892/) (2024)
- [Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel](https://mlsanity.com/paper/2310.03054/) (2023)
- [Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transport](https://mlsanity.com/paper/2402.05443/) (2024)
- [Training Neural Samplers with Reverse Diffusive KL Divergence](https://mlsanity.com/paper/2410.12456/) (2024)

## Abstract (arXiv)

Optimising probabilistic models is a well-studied field in statistics. However, its connection with the training of generative models remains largely under-explored. In this paper, we show that the evolution of time-varying generative models can be projected onto an exponential family manifold, naturally creating a link between the parameters of a generative model and those of a probabilistic model. We then train the generative model by moving its projection on the manifold according to the natural gradient descent scheme. This approach also allows us to efficiently approximate the natural gradient of the KL divergence without relying on MCMC for intractable models. Furthermore, we propose particle versions of the algorithm, which feature closed-form update rules for any parametric model within the exponential family. Through toy and real-world experiments, we validate the effectiveness of the proposed algorithms. The code of the proposed algorithms can be found at https://github.com/anewgithubname/iNGD.