Neon: Negative Extrapolation from Self‑Training

Official repository for our paper Neon: Negative Extrapolation from Self‑Training.

Introduction

Scaling generative AI models is bottlenecked by the scarcity of high-quality training data. The ease of synthesizing from a generative model suggests using (unverified) synthetic data to augment a limited corpus of real data for the purpose of fine-tuning in the hope of improving performance. Unfortunately, however, the resulting positive feedback loop leads to model autophagy disorder (MAD, aka model collapse) that results in a rapid degradation in sample quality and/or diversity. In this paper, we introduce Neon (for Negative Extrapolation frOm self-traiNing), a new learning method that turns the degradation from self-training into a powerful signal for self-improvement. Given a base model, Neon first fine-tunes it on its own self-synthesized data but then, counterintuitively, reverses its gradient updates to extrapolate away from the degraded weights. We prove that Neon works because typical inference samplers that favor high-probability regions create a predictable anti-alignment between the synthetic and real data population gradients, which negative extrapolation corrects to better align the model with the true data distribution. Neon is remarkably easy to implement via a simple post-hoc merge that requires no new real data, works effectively with as few as 1k synthetic samples, and typically uses less than 1% additional training compute. We demonstrate Neon’s universality across a range of architectures (diffusion, flow matching, autoregressive, and inductive moment matching models) and datasets (ImageNet, CIFAR-10, and FFHQ). In particular, on ImageNet 256x256, Neon elevates the xAR-L model to a new state-of-the-art FID of 1.02 with only 0.36% additional training compute.

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Method

In one line: sample with your usual inference to form a synthetic set $S$; briefly fine-tune the reference model on $S$ to get $\theta_s$; then reverse that update with a merge $\theta_{\text{neon}}=(1+w),\theta_r - w,\theta_s$ (small $w>0$), which cancels mode-seeking drift and improves FID.

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Benchmark Performance

Model type	Dataset	Base model FID	Neon FID (paper)	Download model
xAR-L (cond.)	ImageNet-256	1.28	1.02	Download
xAR-B (cond.)	ImageNet-256	1.72	1.31	Download
VAR d16 (cond.)	ImageNet-256	3.30	2.01	Download
VAR d36 (cond.)	ImageNet-512	2.63	1.70	Download
EDM (cond.)	CIFAR-10 (32×32)	1.78	1.38	Download
EDM (uncond.)	CIFAR-10 (32×32)	1.98	1.38	Download
EDM (uncond.)	FFHQ-64×64	2.39	1.12	Download
IMM (cond.)	ImageNet-256	1.99	1.46	Download

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🚀 Quickstart

1) Environment

# from repo root
conda env create -f environment.yml
conda activate neon

2) Download pretrained models & FID stats

bash download_models.sh

This populates checkpoints/ and fid_stats/. Pretrained Neon models can also be downloaded from Hugging Face: https://huggingface.co/sinaalemohammad/Neon

3) Evaluate (FID/IS)

All examples assume 8 GPUs; adjust --nproc_per_node / batch sizes as needed.

xAR @ ImageNet‑256

# 1) VAE for xAR (credit: MAR)
hf download xwen99/mar-vae-kl16 --include kl16.ckpt --local-dir xAR/pretrained
# 2) Use it via:
#   --vae_path xAR/pretrained/kl16.ckpt

# xAR‑L
PYTHONPATH=xAR torchrun --standalone --nproc_per_node=8 xAR/calculate_fid.py \
  --model xar_large \
  --model_ckpt checkpoints/Neon_xARL_imagenet256.pth \
  --cfg 2.3 --vae_path xAR/pretrained/kl16.ckpt \
  --num_images 50000 --batch_size 64 --flow_steps 40 --img_size 256 \
  --fid_stats fid_stats/adm_in256_stats.npz

# xAR‑B
PYTHONPATH=xAR torchrun --standalone --nproc_per_node=8 xAR/calculate_fid.py \
  --model xar_base \
  --model_ckpt checkpoints/Neon_xARB_imagenet256.pth \
  --cfg 2.7 --vae_path xAR/pretrained/kl16.ckpt \
  --num_images 50000 --batch_size 32 --flow_steps 50 --img_size 256 \
  --fid_stats fid_stats/adm_in256_stats.npz

VAR @ ImageNet‑256 / 512

# d16 @ 256
PYTHONPATH=VAR/VAR_imagenet_256 torchrun --standalone --nproc_per_node=8 \
  VAR/VAR_imagenet_256/calculate_fid.py \
  --var_ckpt checkpoints/Neon_VARd16_imagenet256.pth \
  --num_images 50000 --batch_size 64 --img_size 256 \
  --fid_stats fid_stats/adm_in256_stats.npz

# d36 @ 512
PYTHONPATH=VAR/VAR_imagenet_512 torchrun --standalone --nproc_per_node=8 \
  VAR/VAR_imagenet_512/calculate_fid.py \
  --var_ckpt checkpoints/Neon_VARd36_imagenet512.pth \
  --num_images 50000 --batch_size 32 --img_size 512 \
  --fid_stats fid_stats/adm_in512_stats.npz

EDM (Karras et al.) @ CIFAR‑10 / FFHQ

# CIFAR‑10 (conditional)
PYTHONPATH=edm torchrun --standalone --nproc_per_node=8 edm/calculate_fid.py \
  --network_pkl checkpoints/Neon_EDM_conditional_CIFAR10.pkl \
  --ref https://nvlabs-fi-cdn.nvidia.com/edm/fid-refs/cifar10-32x32.npz \
  --seeds 0-49999 --max_batch_size 256 --num_steps 18

# CIFAR‑10 (unconditional)
PYTHONPATH=edm torchrun --standalone --nproc_per_node=8 edm/calculate_fid.py \
  --network_pkl checkpoints/Neon_EDM_unconditional_CIFAR10.pkl \
  --ref https://nvlabs-fi-cdn.nvidia.com/edm/fid-refs/cifar10-32x32.npz \
  --seeds 0-49999 --max_batch_size 256 --num_steps 18

# FFHQ‑64 (unconditional)
PYTHONPATH=edm torchrun --standalone --nproc_per_node=8 edm/calculate_fid.py \
  --network_pkl checkpoints/Neon_EDM_FFHQ.pkl \
  --ref https://nvlabs-fi-cdn.nvidia.com/edm/fid-refs/ffhq-64x64.npz \
  --seeds 0-49999 --max_batch_size 256 --num_steps 40

IMM @ ImageNet‑256

# IMM @ T = 8
PYTHONPATH=imm torchrun --standalone --nproc_per_node=8 imm/calculate_fid.py \
  --model_ckpt checkpoints/Neon_IMM_imagenet256.pth \
  --num_images 50000 --batch_size 64 --img_size 256 \
  --fid_stats fid_stats/adm_in256_stats.npz

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🧪 Toy Experiment (2D Gaussian)

A minimal, visual demo of Neon in action:

• File: toy_appendix.ipynb
• What it does: learns a 2D Gaussian with (i) a tiny diffusion model and (ii) a tiny autoregressive model, then applies Neon to show how the reverse‑merge restores coverage. Great for building intuition

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🗺️ Repository Map

Neon/
├── VAR/                # VAR baselines + eval scripts
├── xAR/                # xAR baselines + eval scripts (uses MAR VAE)
├── edm/                # EDM baselines + metrics/scripts
├── imm/                # IMM baselines + eval scripts
├── toy_appendix.ipynb  # 2D Gaussian toy example (diffusion & AR)
├── download_models.sh  # Grab all checkpoints + FID refs
├── environment.yml     # Reproducible env
└── checkpoints/, fid_stats/ (created by the script)

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📣 Citation

If you find Neon useful, please consider citing the paper:

@article{alemohammadneon2025,
  title   = {Neon: Negative Extrapolation From Self-Training Improves Image Generation},
  author  = {Alemohammad, Sina and Wang, Zhangyang and Baraniuk, Richard G.},
  journal = {arXiv preprint arXiv:2510.03597},
  year    = {2025}
}

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Contact

Questions? Reach out to Sina Alemohammad — [email protected].

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Acknowledgments

This repository builds upon and thanks the following projects:

• VAR — Visual AutoRegressive Modeling
• xAR — Beyond Next‑Token: Next‑X Prediction
• IMM — Inductive Moment Matching
• EDM — Elucidating the Design Space of Diffusion Models
• MAR VAE (KL‑16) tokenizer