QuadTok: Quadtree Visual Tokenizer for Autoregressive Image Generation

Yucheng Mao; Zeyuan Chen; Xiaojun Shan; Xiang Zhang; Divyansh Srivastava; Bingnan Li; Zhuowen Tu

cs.CVOct 7, 2026

QuadTok: Quadtree Visual Tokenizer for Autoregressive Image Generation

Authors: Yucheng Mao, Zeyuan Chen, Xiaojun Shan, Xiang Zhang, Divyansh Srivastava, Bingnan Li, Zhuowen Tu

Organizations: University of California, San Diego

Abstract

We introduce QuadTok, a novel framework for visual tokenization and autoregressive image generation. Compared to traditional approaches using 2D grids or 1D token sequences, we propose a hierarchical quadtree structure, bridging the gap between 2D spatial binding and 1D sequence-level flexibility. The QuadTok tokenizer dynamically allocates representational capacity to visually intricate areas while leaving homogeneous regions at a coarse resolution. Compared with a fixed 256-token grid, our ImageNet-trained tokenizer saves approximately 10% of tokens on ImageNet and 9% when transferred zero-shot to the COCO dataset, while maintaining comparable reconstruction fidelity. Furthermore, the natural causality introduced by the tree structure seamlessly enables autoregressive image generation. Conditioned on a quadtree topology supplied before generation, our 947M GPT-style generative model achieves a 2.08 gFID on the ImageNet $256 \times 256$ benchmark. Additionally, leveraging the strong spatial correlation preserved by the quadtree structure, the QuadTok generator enables zero-shot spatially controlled image generation capabilities. Code: https://github.com/myc634/QuadTok.

Figures & tables

Figure 2: (a) Overview of QuadTok. An image is serialized into a 1D token sequence from a quadtree via breadth-first traversal. ViT features are aggregated into quadtree tokens, quantized, and decoded hierarchically. (b) Hierarchical decoding. Coarse tokens recover global structure; fine tokens refine local regions. (c) Region-wise Complexity Guidance. Complementary probing trees estimate per-region reconstruction benefit to build a content-adaptive quadtree.

Type	Tokenizer	Codebook	ImageNet-1K			COCO
Type	Tokenizer	Codebook	#Tokens	rFID $\downarrow$	PSNR $\uparrow$	#Tokens	rFID $\downarrow$	PSNR $\uparrow$
2D	Taming VQ-GAN ( Esser et al., 2021 )	16384	256	4.98	19.40	256	19.29	19.57
	MaskGIT VQ-GAN ( Chang et al., 2022 )	1024	256	2.28	$-$	–	$-$	$-$
	LlamaGen ( $f=16$ ) ( Sun et al., 2024 )	16384	256	2.19	20.79	256	8.11	20.42
	LlamaGen ( $f=8$ ) ( Sun et al., 2024 )	16384	1024	0.59	24.45	1024	4.19	24.20
1D	TiTok-S ( Yu et al., 2024b )	4096	128	1.71	17.80	128	9.22	17.27

Table 1: Image reconstruction on ImageNet-1K and COCO at

256\times 256

. #Tokens reports dataset-specific mean sequence lengths for QuadTok.

f

denotes the LlamaGen downsampling factor. High-resolution results are provided in Appendix D . – denotes unavailable values.

Tokens	Model	Size	gFID $\downarrow$	IS $\uparrow$	Prec. $\uparrow$	Rec. $\uparrow$
1D	TiTok-S-128–MaskGIT ( Yu et al., 2024b )	287M	1.97	281.80	–	–
	TiTok-S-128–AR ∗ ( Yu et al., 2024b )	775M	4.90	191.71	0.77	0.56
	One-D-Piece-L ∗ ( Miwa et al., 2025b )	775M	2.99	235.10	0.81	0.59
	FlexTok d18-d28 ( Bachmann et al., 2025a )	1.33B	1.86	–	–	–
	GigaTok-B-L ( Xiong et al., 2025 )	1.4B	2.03	238.52	0.80	0.63
	GigaTok-XL-XXL ( Xiong et al., 2025 )	1.4B	1.98	256.76	0.81	0.62

Table 2: Class-conditional generation on ImageNet evaluated at

256\times 256

. These are system-level comparisons with different training and sampling settings. Size denotes generator parameter count. ‡ : native-256 LlamaGen results. xAR and FlowAR use continuous 2D latents.

Figure 5: Zero-shot spatial layout control. Highlighted regions specify where the input quadtree is refined. Generated subjects align with these regions using the frozen ImageNet-trained model.

Target	Topology	Grad-CAM	Box	Mask	FID-50cls
Left	Random	29.6	47.5	51.1	35.03
Left	Prescribed	58.3 (+28.7)	51.8 (+4.3)	59.0 (+7.9)	35.15 (+0.12)
Right	Random	70.4	51.0	48.5	35.03
Right	Prescribed	87.9 (+17.5)	58.1 (+7.1)	55.7 (+7.2)	34.88 (-0.15)
Top	Random	33.9	40.7	42.9	35.03
Top	Prescribed	55.4 (+21.5)	47.0 (+6.3)	47.8 (+4.9)	34.97 (-0.06)

Table 3: Zero-shot spatial control with a frozen ImageNet-trained QuadTok generator. Prescribed vs. random topologies at 192 tokens, 1,000 images each. Grad-CAM, Box, and Mask: % of subjects in the target half-plane (

\uparrow

). FID-50cls (

\downarrow

): against 2,500 class-matched real images.

Table 7

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Type	Tokenizer	#Tokens	Codebook size	rFID $\downarrow$	PSNR $\uparrow$
2D	MaskGIT VQ-GAN ( Chang et al., 2022 )	1024	1024	1.97	–
2D	LlamaGen † ( Sun et al., 2024 )	1024	16384	0.70	23.03
1D	TiTok-L-64 ( Yu et al., 2024b )	64	4096	1.77	–
1D	TiTok-B-128 ( Yu et al., 2024b )	128	4096	1.52	–
Quadtree	QuadTok	987	16384	0.84	24.96

Appendix

Table 6: ImageNet-1K reconstruction with

512\times 512

inputs. #Tokens is the mean for QuadTok. † : LlamaGen resizes reconstructions to

256\times 256

for evaluation. MaskGIT and TiTok values follow Table 2 of the TiTok paper. – denotes unreported values.

Model	Size	gFID $\downarrow$	IS $\uparrow$	Precision $\uparrow$	Recall $\uparrow$
DiT-XL/2 ( Peebles and Xie, 2023 )	675M	3.04	240.82	0.84	0.54
CAT ( Shen et al., 2025 )	$\approx$ 431M	4.38	181.03	0.76	0.48
TiTok-B-128 ( Yu et al., 2024b ) -MaskGIT	177M	2.13	261.2	–	–
VAR- $d36$ -s ( Tian et al., 2024 )	2.3B	2.63	303.2	–	–
QuadTok	344M	2.734	268.01	0.835	0.537

Appendix

Table 7: Class-conditional ImageNet generation at

512\times 512

. Size denotes generator parameters. CAT uses a continuous VAE with DiT (

c=8

, original Table 7); TiTok uses MaskGIT with 64 sampling steps. VAR uses next-scale prediction, while QuadTok uses causal autoregressive decoding. Results are system-level comparisons; – denotes unreported metrics.

Parameters	$p=0.25$	$p=0.50$	$p=0.75$
Approx. tokens	128	192	255
111M	1.81–2.40 $\times$	1.14–1.58 $\times$	1.20 $\times$
343M	1.62–1.94 $\times$	1.09–1.20 $\times$	1.09 $\times$
775M	1.57–1.91 $\times$	1.15–1.21 $\times$	1.10 $\times$

Appendix

Table 8: Generation speedup relative to LlamaGen. The LlamaGen timing baseline uses randomly initialized generator weights in the

256\times 256

configuration and generates 256 tokens. At

p=0.25

and

0.50

, ranges span batch sizes 1/32 and CFG scales 1/2. The

p=0.75

column reports the near-equal-token comparison. Ratios measure autoregressive generation, excluding image decoding; values above 1 indicate faster generation. The 775M comparison is timing-only ( Appendix E ).

Scale	Method	Tokens	Gen. (s)	+ decode (s)	Speedup
111M	LlamaGen	256.0	5.440	5.551	1.00 $\times$
111M	QuadTok ( $p=0.25$ )	126.6	2.524	2.560	2.16 $\times$
111M	QuadTok ( $p=0.50$ )	189.2	3.528	3.570	1.54 $\times$
111M	QuadTok ( $p=0.75$ )	255.0	4.533	4.586	1.20 $\times$
343M	LlamaGen	256.0	8.404	8.512	1.00 $\times$
343M	QuadTok ( $p=0.25$ )	126.6	4.656	4.692	1.80 $\times$

Appendix

Table 9: Absolute generation latency at batch size 32 and CFG scale 2. Means over 50 timed batches, in seconds per batch. Gen. denotes autoregressive sampling; + decode includes image decoding. Results cover

p=0.25

0.50

, and

0.75

under the protocol in Appendix E . Speedup is the ratio of LlamaGen to QuadTok generation latency.

Tokenizer	Tokens/image	Batch 32	Batch 128
LlamaGen VQ-16	256	2.927	2.885
TiTok L-32	32	1.480	1.352
TiTok B-64	64	0.586	0.512
TiTok S-128	128	0.305	0.277
QuadTok	234.3 / 233.2	8.795	6.186

Appendix

Table 10: Pretokenization latency at

256\times 256

. Mean milliseconds per image on one A100-80GB GPU. Token counts for QuadTok are measured on the timed batches (32 / 128); fixed encoders use a constant budget. Timing includes adaptive selection for QuadTok and ends at discrete codes, before reconstruction decoding.

Guidance Metric	Threshold ( $\tau$ )	#Tokens $\downarrow$	rFID $\downarrow$	PSNR $\uparrow$
$\mathcal{L}_{\mathrm{MSE}}$	0.0005	230	1.67	20.52
$\mathcal{L}_{\mathrm{LPIPS}}$	0.03	267	1.46	20.24
	0.05	230	1.46	20.37
	0.06	195	1.75	19.99
Combined ( $\mathcal{L}_{\mathrm{MSE}}\times 10+\mathcal{L}_{\mathrm{LPIPS}}$ )	0.06	230	1.58	20.37

Appendix

Table 11: Ablation of complexity guidance metric and threshold

\tau

. We compare MSE, LPIPS, and their linear combination as probing metrics; for LPIPS we sweep the expansion threshold

\tau

, and report MSE and the combination at a matched

\sim

230-token budget on ImageNet-1K. LPIPS at

\tau{=}0.05

achieves the best perceptual quality (rFID

1.46

) at

230

tokens, and is adopted as the default.

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One-dimensional (1D) variable-length visual tokenizers enable adaptive compression by varying the number of tokens, allowing downstream autoregressive (AR) models to flexibly trade off generation quality against computational cost using a single tokenizer. However, existing approaches based on nested dropout often fail to fully exploit the representational capacity of the tokenizer, resulting in suboptimal performance in both image reconstruction and generation. In this work, we introduce NesTok, a nested self-alignment framework tailored to dynamic visual tokenizers. NesTok introduces cross-length training, which jointly optimizes reconstruction across token lengths while using the full-length sequence to guide shorter counterparts, enabling shorter token sequences to approach the reconstruction quality of full-length sequences. On ImageNet, NesTok improves substantially over standard training and achieves an rFID score of 0.98. On downstream image generation, it achieves the state-of-the-art gFID score of 1.46 on ImageNet 256

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