# Conditionally Strongly Log-Concave Generative Models

arXiv: https://arxiv.org/abs/2306.00181 · HTML: https://mlsanity.com/paper/2306.00181/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 26 of 26)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Statistical Efficiency of Score Matching: The View from Isoperimetry](https://mlsanity.com/paper/2210.00726/) (2022)
- [Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlo](https://mlsanity.com/paper/2202.05214/) (2022)
- [Wavelet Score-Based Generative Modeling](https://mlsanity.com/paper/2208.05003/) (2022)
- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [Density Estimation in Infinite Dimensional Exponential Families](https://mlsanity.com/paper/1312.3516/) (2013)
- [Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices](https://mlsanity.com/paper/1912.10754/) (2019)
- [Wavelet Flow: Fast Training of High Resolution Normalizing Flows](https://mlsanity.com/paper/2010.13821/) (2020)
- [Learning multi-scale local conditional probability models of images](https://mlsanity.com/paper/2303.02984/) (2023)
- [SWAGAN: A Style-based Wavelet-driven Generative Model](https://mlsanity.com/paper/2102.06108/) (2021)
- [Non-Gaussian information from weak lensing data via deep learning](https://mlsanity.com/paper/1802.01212/) (2018)
- [Fast Mixing of Multi-Scale Langevin Dynamics under the Manifold Hypothesis](https://mlsanity.com/paper/2006.11166/) (2020)
- [Wavelet Conditional Renormalization Group](https://mlsanity.com/paper/2207.04941/) (2022)
- [Efficient and principled score estimation with Nystr"om kernel exponential families](https://mlsanity.com/paper/1705.08360/) (2017)
- [On Energy-Based Models with Overparametrized Shallow Neural Networks](https://mlsanity.com/paper/2104.07531/) (2021)

## Built on by (most cited first, 2 of 2)

- [Hierarchic Flows to Estimate and Sample High-dimensional Probabilities](https://mlsanity.com/paper/2405.03468/) (2024)
- [Overcoming critical slowing down in frustrated spin systems by learned multiscale sampling](https://mlsanity.com/paper/2608.31114/) (2026)

## Abstract (arXiv)

There is a growing gap between the impressive results of deep image generative models and classical algorithms that offer theoretical guarantees. The former suffer from mode collapse or memorization issues, limiting their application to scientific data. The latter require restrictive assumptions such as log-concavity to escape the curse of dimensionality. We partially bridge this gap by introducing conditionally strongly log-concave (CSLC) models, which factorize the data distribution into a product of conditional probability distributions that are strongly log-concave. This factorization is obtained with orthogonal projectors adapted to the data distribution. It leads to efficient parameter estimation and sampling algorithms, with theoretical guarantees, although the data distribution is not globally log-concave. We show that several challenging multiscale processes are conditionally log-concave using wavelet packet orthogonal projectors. Numerical results are shown for physical fields such as the varphi4 model and weak lensing convergence maps with higher resolution than in previous works.