# Fast Score-Based Sampling via Log-Concave Reductions

arXiv: https://arxiv.org/abs/2512.24152 · HTML: https://mlsanity.com/paper/2512.24152/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 55 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 30 of 33)

- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Error Bounds for Flow Matching Methods](https://mlsanity.com/paper/2305.16860/) (2023)
- [Convergence of Langevin MCMC in KL-divergence](https://mlsanity.com/paper/1705.09048/) (2017)
- [Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models](https://mlsanity.com/paper/2306.09251/) (2023)
- [The Randomized Midpoint Method for Log-Concave Sampling](https://mlsanity.com/paper/1909.05503/) (2019)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models](https://mlsanity.com/paper/2408.02320/) (2024)
- [Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradients](https://mlsanity.com/paper/1905.12247/) (2019)
- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel](https://mlsanity.com/paper/2406.00924/) (2024)
- [Minimax Optimality of the Probability Flow ODE for Diffusion Models](https://mlsanity.com/paper/2503.09583/) (2025)
- [Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference](https://mlsanity.com/paper/2405.16387/) (2024)
- [An Efficient Sampling Algorithm for Non-smooth Composite Potentials](https://mlsanity.com/paper/1910.00551/) (2019)

## Built on by (most cited first, 4 of 4)

- [High-accuracy sampling for diffusion models and log-concave distributions](https://mlsanity.com/paper/2602.01338/) (2026)
- [High-accuracy and dimension-free sampling with diffusions](https://mlsanity.com/paper/2601.10708/) (2026)
- [Denoising growth complexity: Data geometry and certified schedules for diffusion sampling](https://mlsanity.com/paper/2607.26285/) (2026)
- [Nonparametric undirected graphical model selection using diffusion models](https://mlsanity.com/paper/2606.08468/) (2026)

## Abstract (arXiv)

Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities. It depends on availability of (approximate) Stein score functions for various levels of additive noise. We show how in some generality, the availability of scores allows the general problem to be ``reduced'' to sampling from an adaptively constructed sequence of K strongly log-concave (SLC) sub-problems. The reduction is simple, constructive and algorithm-independent, so that any SLC sampler can be used as a subroutine. Various bounds on score-based sampling complexity follow directly: for instance, high-accuracy SLC samplers yield tildeO(K √d operatornamepolylog(1/varepsilon)) guarantees for accuracy varepsilon in dimension d, where randomized midpoint SLC schemes yield tildeO(K d1/3 operatornamepoly(1/varepsilon)) guarantees. When the original distribution itself is SLC, we prove that K ≤ 1 + log2(kappa), thereby obtaining the first efficient procedure with logarithmic dependence on condition number kappa; for general distributions, the quantity K depends on the geometry of score Hessian across the trajectory. Our analysis is direct and simple, involving techniques and insights complementary to those in standard analyses of discretized diffusions.