# SNCE: Geometry-Aware Supervision for Scalable Discrete Image Generation

arXiv: https://arxiv.org/abs/2603.15150 · HTML: https://mlsanity.com/paper/2603.15150/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 66 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 30 of 59)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [Emerging Properties in Unified Multimodal Pretraining](https://mlsanity.com/paper/2505.14683/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Janus-Pro: Unified Multimodal Understanding and Generation with Data and Model Scaling](https://mlsanity.com/paper/2501.17811/) (2025)
- [Emu3: Next-Token Prediction is All You Need](https://mlsanity.com/paper/2409.18869/) (2024)
- [Autoregressive Model Beats Diffusion: Llama for Scalable Image Generation](https://mlsanity.com/paper/2406.06525/) (2024)
- [Show-o: One Single Transformer to Unify Multimodal Understanding and Generation](https://mlsanity.com/paper/2408.12528/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [MagicBrush: A Manually Annotated Dataset for Instruction-Guided Image Editing](https://mlsanity.com/paper/2306.10012/) (2023)
- [ELLA: Equip Diffusion Models with LLM for Enhanced Semantic Alignment](https://mlsanity.com/paper/2403.05135/) (2024)
- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [Step1X-Edit: A Practical Framework for General Image Editing](https://mlsanity.com/paper/2504.17761/) (2025)
- [OmniGen: Unified Image Generation](https://mlsanity.com/paper/2409.11340/) (2024)

## Built on by (most cited first, 1 of 1)

- [Nemotron-Labs-Diffusion-Image: Advancing Masked Discrete Diffusion for High-Resolution Image Synthesis](https://mlsanity.com/paper/2606.29814/) (2026)

## Abstract (arXiv)

Recent advancements in discrete image generation showed that scaling the VQ codebook size significantly improves reconstruction fidelity. However, training generative models with a large VQ codebook remains challenging, typically requiring larger model size and a longer training schedule. In this work, we propose Stochastic Neighbor Cross Entropy Minimization (SNCE), a novel training objective designed to address the optimization challenges of large-codebook discrete image generators. Instead of supervising the model with a hard one-hot target, SNCE constructs a soft categorical distribution over a set of neighboring tokens. The probability assigned to each token is proportional to the proximity between its code embedding and the ground-truth image embedding, encouraging the model to capture semantically meaningful geometric structure in the quantized embedding space. We conduct extensive experiments across class-conditional ImageNet-256 generation, large-scale text-to-image synthesis, and image editing tasks. Results show that SNCE significantly improves convergence speed and overall generation quality compared to standard cross-entropy objectives.