# DISK: Differentiable Sparse Kernel Complex for Efficient Spatially-Variant Convolution

arXiv: https://arxiv.org/abs/2512.04556 · HTML: https://mlsanity.com/paper/2512.04556/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [Video Frame Interpolation via Adaptive Convolution](https://mlsanity.com/paper/1703.07514/) (2017)
- [Burst Denoising with Kernel Prediction Networks](https://mlsanity.com/paper/1712.02327/) (2017)
- [Spatio-Temporal Filter Adaptive Network for Video Deblurring](https://mlsanity.com/paper/1904.12257/) (2019)
- [Decoupled Dynamic Filter Networks](https://mlsanity.com/paper/2104.14107/) (2021)
- [Revisiting Dynamic Convolution via Matrix Decomposition](https://mlsanity.com/paper/2103.08756/) (2021)
- [DoF-NeRF: Depth-of-Field Meets Neural Radiance Fields](https://mlsanity.com/paper/2208.00945/) (2022)
- [LKD-Net: Large Kernel Convolution Network for Single Image Dehazing](https://mlsanity.com/paper/2209.01788/) (2022)
- [Spatially-Variant CNN-based Point Spread Function Estimation for Blind Deconvolution and Depth Estimation in Optical Microscopy](https://mlsanity.com/paper/2010.04011/) (2020)

## Abstract (arXiv)

Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations, such as simulated annealing or low-rank decompositions, either lack efficiency or fail to capture non-convex kernels. We introduce a differentiable kernel decomposition framework that represents a target spatially-variant, dense, complex kernel using a set of sparse kernel samples. Our approach features (i) a decomposition that enables differentiable optimization of sparse kernels, (ii) a dedicated initialization strategy for non-convex shapes to avoid poor local minima, and (iii) a kernel-space interpolation scheme that extends single-kernel filtering to spatially varying filtering without retraining and additional runtime overhead. Experiments on Gaussian and non-convex kernels show that our method achieves higher fidelity than simulated annealing and significantly lower cost than low-rank decompositions. Our approach provides a practical solution for mobile imaging and real-time rendering, while remaining fully differentiable for integration into broader learning pipelines.