# Geometry-Based Data Generation

arXiv: https://arxiv.org/abs/1802.04927 · HTML: https://mlsanity.com/paper/1802.04927/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2018.

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

- [scDiffusion: conditional generation of high-quality single-cell data using diffusion model](https://mlsanity.com/paper/2401.03968/) (2024)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [Manifold Alignment with Label Information](https://mlsanity.com/paper/2210.12774/) (2022)
- [A Computability Perspective on (Verified) Machine Learning](https://mlsanity.com/paper/2102.06585/) (2021)
- [Single-Cell RNA-seq Synthesis with Latent Diffusion Model](https://mlsanity.com/paper/2312.14220/) (2023)
- [Adaptive Neighbourhoods for the Discovery of Adversarial Examples](https://mlsanity.com/paper/2101.09108/) (2021)
- [Imbalanced Classification via Explicit Gradient Learning From Augmented Data](https://mlsanity.com/paper/2202.10550/) (2022)
- [Imbalanced Classification via a Tabular Translation GAN](https://mlsanity.com/paper/2204.08683/) (2022)
- [JIR-Arena: The First Benchmark Dataset for Just-in-time Information Recommendation](https://mlsanity.com/paper/2505.13550/) (2025)
- [RNAGenScape: Property-Guided, Optimized Generation of mRNA Sequences with Manifold Langevin Dynamics](https://mlsanity.com/paper/2510.24736/) (2025)
- [Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment](https://mlsanity.com/paper/2602.00974/) (2026)

## Abstract (arXiv)

Many generative models attempt to replicate the density of their input data. However, this approach is often undesirable, since data density is highly affected by sampling biases, noise, and artifacts. We propose a method called SUGAR (Synthesis Using Geometrically Aligned Random-walks) that uses a diffusion process to learn a manifold geometry from the data. Then, it generates new points evenly along the manifold by pulling randomly generated points into its intrinsic structure using a diffusion kernel. SUGAR equalizes the density along the manifold by selectively generating points in sparse areas of the manifold. We demonstrate how the approach corrects sampling biases and artifacts, while also revealing intrinsic patterns (e.g. progression) and relations in the data. The method is applicable for correcting missing data, finding hypothetical data points, and learning relationships between data features.