# Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flows

arXiv: https://arxiv.org/abs/2305.02164 · HTML: https://mlsanity.com/paper/2305.02164/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 69 references that are in the map.
- First posted on arXiv 3 May 2023.

## Builds on (most cited first, 30 of 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [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)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [ERNIE-ViLG 2.0: Improving Text-to-Image Diffusion Model with Knowledge-Enhanced Mixture-of-Denoising-Experts](https://mlsanity.com/paper/2210.15257/) (2022)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions](https://mlsanity.com/paper/1806.08141/) (2018)
- [Subspace Diffusion Generative Models](https://mlsanity.com/paper/2205.01490/) (2022)
- [Distributional Sliced-Wasserstein and Applications to Generative Modeling](https://mlsanity.com/paper/2002.07367/) (2020)

## Built on by (most cited first, 15 of 15)

- [Generative Sliced MMD Flows with Riesz Kernels](https://mlsanity.com/paper/2305.11463/) (2023)
- [Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching](https://mlsanity.com/paper/2403.18705/) (2024)
- [Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel](https://mlsanity.com/paper/2310.03054/) (2023)
- [Sliced Wasserstein with Random-Path Projecting Directions](https://mlsanity.com/paper/2401.15889/) (2024)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction](https://mlsanity.com/paper/2312.16611/) (2023)
- [Neural Sinkhorn Gradient Flow](https://mlsanity.com/paper/2401.14069/) (2024)
- [Fast Kernel Summation in High Dimensions via Slicing and Fourier Transforms](https://mlsanity.com/paper/2401.08260/) (2024)
- [DDEQs: Distributional Deep Equilibrium Models through Wasserstein Gradient Flows](https://mlsanity.com/paper/2503.01140/) (2025)
- [Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances](https://mlsanity.com/paper/2310.13433/) (2023)
- [Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flow](https://mlsanity.com/paper/2406.15762/) (2024)
- [Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis](https://mlsanity.com/paper/2502.06525/) (2025)
- [Convergence Rates for Distribution Matching with Sliced Optimal Transport](https://mlsanity.com/paper/2602.10691/) (2026)
- [Liouville PDE-based sliced-Wasserstein flow](https://mlsanity.com/paper/2505.17204/) (2025)
- [Difference of Convex Programming in the Wasserstein Space with Applications to MMD Optimization](https://mlsanity.com/paper/2606.27767/) (2026)

## Abstract (arXiv)

Sliced-Wasserstein Flow (SWF) is a promising approach to nonparametric generative modeling but has not been widely adopted due to its suboptimal generative quality and lack of conditional modeling capabilities. In this work, we make two major contributions to bridging this gap. First, based on a pleasant observation that (under certain conditions) the SWF of joint distributions coincides with those of conditional distributions, we propose Conditional Sliced-Wasserstein Flow (CSWF), a simple yet effective extension of SWF that enables nonparametric conditional modeling. Second, we introduce appropriate inductive biases of images into SWF with two techniques inspired by local connectivity and multiscale representation in vision research, which greatly improve the efficiency and quality of modeling images. With all the improvements, we achieve generative performance comparable with many deep parametric generative models on both conditional and unconditional tasks in a purely nonparametric fashion, demonstrating its great potential.