# cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs

arXiv: https://arxiv.org/abs/2102.08463 · HTML: https://mlsanity.com/paper/2102.08463/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2021.

## Built on by (most cited first, 11 of 11)

- [Beyond Regular Grids: Fourier-Based Neural Operators on Arbitrary Domains](https://mlsanity.com/paper/2305.19663/) (2023)
- [Fast Summation of Radial Kernels via QMC Slicing](https://mlsanity.com/paper/2410.01316/) (2024)
- [Training Adaptive Reconstruction Networks for Blind Inverse Problems](https://mlsanity.com/paper/2202.11342/) (2022)
- [Fast kernel methods: Sobolev, physics-informed, and additive models](https://mlsanity.com/paper/2509.02649/) (2025)
- [Scaling and Acceleration of Three-dimensional Structure Determination for Single-Particle Imaging Experiments with SpiniFEL](https://mlsanity.com/paper/2109.05339/) (2021)
- [StoDIP: Efficient 3D MRF image reconstruction with deep image priors and stochastic iterations](https://mlsanity.com/paper/2408.02367/) (2024)
- [Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions](https://mlsanity.com/paper/2207.13674/) (2022)
- [GrINd: Grid Interpolation Network for Scattered Observations](https://mlsanity.com/paper/2403.19570/) (2024)
- [A New k-Space Model for Non-Cartesian Fourier Imaging](https://mlsanity.com/paper/2505.05647/) (2025)
- [Joint Denoising of Cryo-EM Projection Images using Polar Transformers](https://mlsanity.com/paper/2506.11283/) (2025)
- [SOLVAR: Fast covariance-based heterogeneity analysis with pose refinement for cryo-EM](https://mlsanity.com/paper/2602.17603/) (2026)

## Abstract (arXiv)

Nonuniform fast Fourier transforms dominate the computational cost in many applications including image reconstruction and signal processing. We thus present a general-purpose GPU-based CUDA library for type 1 (nonuniform to uniform) and type 2 (uniform to nonuniform) transforms in dimensions 2 and 3, in single or double precision. It achieves high performance for a given user-requested accuracy, regardless of the distribution of nonuniform points, via cache-aware point reordering, and load-balanced blocked spreading in shared memory. At low accuracies, this gives on-GPU throughputs around 109 nonuniform points per second, and (even including host-device transfer) is typically 4-10× faster than the latest parallel CPU code FINUFFT (at 28 threads). It is competitive with two established GPU codes, being up to 90× faster at high accuracy and/or type 1 clustered point distributions. Finally we demonstrate a 5-12× speedup versus CPU in an X-ray diffraction 3D iterative reconstruction task at 10-12 accuracy, observing excellent multi-GPU weak scaling up to one rank per GPU.