# PCA-VAE: Differentiable Subspace Quantization without Codebook Collapse

arXiv: https://arxiv.org/abs/2602.18904 · HTML: https://mlsanity.com/paper/2602.18904/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 21 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [VideoGPT: Video Generation using VQ-VAE and Transformers](https://mlsanity.com/paper/2104.10157/) (2021)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Finite Scalar Quantization: VQ-VAE Made Simple](https://mlsanity.com/paper/2309.15505/) (2023)
- [MAGVIT: Masked Generative Video Transformer](https://mlsanity.com/paper/2212.05199/) (2022)
- [Addressing Representation Collapse in Vector Quantized Models with One Linear Layer](https://mlsanity.com/paper/2411.02038/) (2024)
- [Memory Limited, Streaming PCA](https://mlsanity.com/paper/1307.0032/) (2013)
- [Streaming PCA and Subspace Tracking: The Missing Data Case](https://mlsanity.com/paper/1806.04609/) (2018)
- [On the Optimality of the Oja's Algorithm for Online PCA](https://mlsanity.com/paper/2104.00512/) (2021)

## Abstract (arXiv)

Vector-quantized autoencoders deliver high-fidelity latents but suffer inherent flaws: the quantizer is non-differentiable, requires straight-through hacks, and is prone to collapse. We address these issues at the root by replacing VQ with a simple, principled, and fully differentiable alternative: an online PCA bottleneck trained via Oja's rule. The resulting model, PCA-VAE, learns an orthogonal, variance-ordered latent basis without codebooks, commitment losses, or lookup noise. Despite its simplicity, PCA-VAE exceeds VQ-GAN and SimVQ in reconstruction quality on CelebAHQ while using 10-100x fewer latent bits. It also produces naturally interpretable dimensions (e.g., pose, lighting, gender cues) without adversarial regularization or disentanglement objectives. These results suggest that PCA is a viable replacement for VQ: mathematically grounded, stable, bit-efficient, and semantically structured, offering a new direction for generative models beyond vector quantization.