# Local Curvature Smoothing with Stein's Identity for Efficient Score Matching

arXiv: https://arxiv.org/abs/2412.03962 · HTML: https://mlsanity.com/paper/2412.03962/

## 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 28 of its 40 references that are in the map.
- First posted on arXiv 5 Dec 2024.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [RNADE: The real-valued neural autoregressive density-estimator](https://mlsanity.com/paper/1306.0186/) (2013)
- [Gradient Estimators for Implicit Models](https://mlsanity.com/paper/1705.07107/) (2017)
- [Efficient Learning of Generative Models via Finite-Difference Score Matching](https://mlsanity.com/paper/2007.03317/) (2020)
- [A Spectral Approach to Gradient Estimation for Implicit Distributions](https://mlsanity.com/paper/1806.02925/) (2018)
- [Maximum Likelihood Training of Implicit Nonlinear Diffusion Models](https://mlsanity.com/paper/2205.13699/) (2022)
- [FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation](https://mlsanity.com/paper/2210.04296/) (2022)
- [AR-DAE: Towards Unbiased Neural Entropy Gradient Estimation](https://mlsanity.com/paper/2006.05164/) (2020)

## Abstract (arXiv)

The training of score-based diffusion models (SDMs) is based on score matching. The challenge of score matching is that it includes a computationally expensive Jacobian trace. While several methods have been proposed to avoid this computation, each has drawbacks, such as instability during training and approximating the learning as learning a denoising vector field rather than a true score. We propose a novel score matching variant, local curvature smoothing with Stein's identity (LCSS). The LCSS bypasses the Jacobian trace by applying Stein's identity, enabling regularization effectiveness and efficient computation. We show that LCSS surpasses existing methods in sample generation performance and matches the performance of denoising score matching, widely adopted by most SDMs, in evaluations such as FID, Inception score, and bits per dimension. Furthermore, we show that LCSS enables realistic image generation even at a high resolution of 1024 × 1024.