---
pipeline_tag: text-to-image
library_name: pytorch
---

# SphereAR: Hyperspherical Latents Improve Continuous-Token Autoregressive Generation

This repository contains the official PyTorch implementation of the paper [Hyperspherical Latents Improve Continuous-Token Autoregressive Generation](https://huggingface.co/papers/2509.24335).

The official code and further details can be found on the GitHub repository: [https://github.com/guolinke/SphereAR](https://github.com/guolinke/SphereAR)

## Abstract
Autoregressive (AR) models are promising for image generation, yet continuous-token AR variants often trail latent diffusion and masked-generation models. The core issue is heterogeneous variance in VAE latents, which is amplified during AR decoding, especially under classifier-free guidance (CFG), and can cause variance collapse. We propose SphereAR to address this issue. Its core design is to constrain all AR inputs and outputs -- including after CFG -- to lie on a fixed-radius hypersphere (constant $\ell_2$ norm), leveraging hyperspherical VAEs. Our theoretical analysis shows that hyperspherical constraint removes the scale component (the primary cause of variance collapse), thereby stabilizing AR decoding. Empirically, on ImageNet generation, SphereAR-H (943M) sets a new state of the art for AR models, achieving FID 1.34. Even at smaller scales, SphereAR-L (479M) reaches FID 1.54 and SphereAR-B (208M) reaches 1.92, matching or surpassing much larger baselines such as MAR-H (943M, 1.55) and VAR-d30 (2B, 1.92). To our knowledge, this is the first time a pure next-token AR image generator with raster order surpasses diffusion and masked-generation models at comparable parameter scales.

<p align="center">
<img src="https://github.com/guolinke/SphereAR/raw/main/figures/grid.jpg" width=780>
<p>

## Introduction
SphereAR is a simple yet effective approach to continuous-token autoregressive (AR) image generation: it makes AR scale-invariant by constraining all AR inputs and outputs---**including after CFG**---to lie on a fixed-radius hypersphere (constant L2 norm) via hyperspherical VAEs.

The model is a **pure next-token** AR generator with **raster** order, matching standard language AR modeling (i.e., it is *not* next-scale AR like VAR and *not* next-set AR like MAR/MaskGIT).

On ImageNet 256×256, SphereAR achieves a state-of-the-art FID of **1.34** among AR image generators.

## Model Checkpoints
The following pre-trained models are available for class-conditional image generation on ImageNet:

| Name | params | FID (256x256) | weight |
|---|:---:|:---:|:---:|
| S-VAE | 75M | - | [vae.pt](https://huggingface.co/guolinke/SphereAR/blob/main/vae.pt) |
| SphereAR-B | 208M | 1.92 | [SphereAR_B.pt](https://huggingface.co/guolinke/SphereAR/blob/main/SphereAR_B.pt) |
| SphereAR-L | 479M | 1.54 | [SphereAR_L.pt](https://huggingface.co/guolinke/SphereAR/blob/main/SphereAR_L.pt) |
| SphereAR-H | 943M | 1.34 | [SphereAR_H.pt](https://huggingface.co/guolinke/SphereAR/blob/main/SphereAR_H.pt) |

For detailed instructions on evaluation and training using these checkpoints, please refer to the [official GitHub repository](https://github.com/guolinke/SphereAR).

## Citation
If you find this work useful, please consider citing the paper:

```bibtex
@article{ke2025hyperspherical,
   title={Hyperspherical Latents Improve Continuous-Token Autoregressive Generation}, 
   author={Guolin Ke and Hui Xue},
   journal={arXiv preprint arXiv:2509.24335},
   year={2025}
}
```