# Bespoke Non-Stationary Solvers for Fast Sampling of Diffusion and Flow Models

arXiv: https://arxiv.org/abs/2403.01329 · HTML: https://mlsanity.com/paper/2403.01329/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 2 Mar 2024.

## 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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing](https://mlsanity.com/paper/2110.13900/) (2021)
- [Common Voice: A Massively-Multilingual Speech Corpus](https://mlsanity.com/paper/1912.06670/) (2019)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [EXPRESSO: A Benchmark and Analysis of Discrete Expressive Speech Resynthesis](https://mlsanity.com/paper/2308.05725/) (2023)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Optimal Linear Subspace Search: Learning to Construct Fast and High-Quality Schedulers for Diffusion Models](https://mlsanity.com/paper/2305.14677/) (2023)

## Built on by (most cited first, 10 of 10)

- [Video Diffusion Models: A Survey](https://mlsanity.com/paper/2405.03150/) (2024)
- [S4S: Solving for a Diffusion Model Solver](https://mlsanity.com/paper/2502.17423/) (2025)
- [Parallel Decoding Distillation for Fast Image and Video Generation](https://mlsanity.com/paper/2607.26004/) (2026)
- [Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolation](https://mlsanity.com/paper/2503.10103/) (2025)
- [DyWeight: Dynamic Gradient Weighting for Few-Step Diffusion Sampling](https://mlsanity.com/paper/2603.11607/) (2026)
- [Few-Step Diffusion Sampling Through Instance-Aware Discretizations](https://mlsanity.com/paper/2603.17671/) (2026)
- [A universal vision transformer for fast calorimeter simulations](https://mlsanity.com/paper/2601.05289/) (2026)
- [Dual-Solver: A Generalized ODE Solver for Diffusion Models with Dual Prediction](https://mlsanity.com/paper/2603.03973/) (2026)
- [Learning to Solve Generative ODEs Beyond the Linear Span](https://mlsanity.com/paper/2606.08672/) (2026)
- [A Step in the Right Place: Understanding and Optimizing Timestep Placement in Continuous Diffusion Language Models](https://mlsanity.com/paper/2610.15527/) (2026)

## Abstract (arXiv)

This paper introduces Bespoke Non-Stationary (BNS) Solvers, a solver distillation approach to improve sample efficiency of Diffusion and Flow models. BNS solvers are based on a family of non-stationary solvers that provably subsumes existing numerical ODE solvers and consequently demonstrate considerable improvement in sample approximation (PSNR) over these baselines. Compared to model distillation, BNS solvers benefit from a tiny parameter space (<200 parameters), fast optimization (two orders of magnitude faster), maintain diversity of samples, and in contrast to previous solver distillation approaches nearly close the gap from standard distillation methods such as Progressive Distillation in the low-medium NFE regime. For example, BNS solver achieves 45 PSNR / 1.76 FID using 16 NFE in class-conditional ImageNet-64. We experimented with BNS solvers for conditional image generation, text-to-image generation, and text-2-audio generation showing significant improvement in sample approximation (PSNR) in all.