BAR: Refactor the Basis of Autoregressive Visual Generation
Authors: Zhicong Tang
Dong Chen
Jianmin Bao
Baining Guo
Venue: ICLR 2026 Poster (2026)
Keywords: Autoregressive Models
Autoregressive Visual Generation
Primary area: generative models
TL;DR: This work proposes BAR to adaptively refactor tokens, learn transforms, and achieve SOTA on image generation.

Abstract: Autoregressive (AR) models, despite their remarkable successes, encounter limitations in image generation due to sequential prediction of tokens, e.g. local image patches, in a predetermined row-major raster-scan order. Prior works improve AR with various designs of prediction units and orders, however, rely on human inductive biases. This work proposes Basis Autoregressive (BAR), a novel paradigm that conceptualizes tokens as basis vectors within the image space and employs an end-to-end learnable approach to transform basis. By viewing tokens $x_k$ as the projection of image $\mathbf{x}$ onto basis vectors $e_k$, BAR's unified framework refactors fixed token sequences through the linear transform $\mathbf{y}=\mathbf{Ax}$, and encompasses previous methods as specific instances of matrix $\mathbf{A}$. Furthermore, BAR adaptively optimizes the transform matrix with an end-to-end AR objective, thereby discovering effective strategies beyond hand-crafted assumptions. Comprehensive experiments, notably achieving a state-of-the-art FID of 1.15 on the ImageNet-256 benchmark, demonstrate the ability of BAR to overcome human biases and significantly advance image generation, including text-to-image synthesis.

Published as a conference paper at ICLR 2026
BAR: REFACTOR THE BASIS OF AUTOREGRESSIVE VISUAL GENERATION
Zhicong Tang Tsinghua University
Dong Chen Microsoft Research Asia
Jianmin Bao
Microsoft Research Asia
Baining Guo
Microsoft Research Asia
ABSTRACT
Autoregressive (AR) models, despite their remarkable successes, encounter limi- tations image generation due to sequential prediction of tokens, egg. local image patches, in predetermined row-major raster-scan order. Prior works improve AR with various designs of prediction units and orders, however, rely on human in- ductive biases. This work proposes Basis Autoregressive (BAR), novel paradigm that conceptualizes tokens as basis vectors within the image space and employs an end-to-end learnable approach to transform basis. By viewing tokens 24 the projection image x onto basis vectors ck2 BAR's s unified framework refactors fixed token sequences through the linear transform y Ax, and encompasses previous methods as specific instances of matrix A. Furthermore, BAR adaptively optimizes the transform matrix with end-to-end AR objective, thereby discov- ering effective strategies beyond hand-crafted assumptions. Comprehensive ex- periments, notably achieving state-of-the-ar FID of 1.15 on the ImageNet-256 benchmark, demonstrate the ability of BAR to overcome human biases and sig- nificantly advance image generation, including text-to- to-image synthesis.
INTRODUCTION
Autoregressive (AR) models have demonstrated remarkable success in various domains (OpenAl, 2022 Team et al. 2023). particularly in natural language processing (Brown et al. 2020 Dev in et al. 2019 Raffel et al. 2020). This paradigm of sequentially predicting next tokens is extended to the vision domain with notable progress (Alayrac et al.) 2022, Yu et al., 2022), including image generation (Esser et al. 2021 Ramesh et al., 202 Han et al. 2024| Yu al. 2024a), and even surpasses diffusion models (Song et al. 2021 Ho et al. 2020; Podell et al. 2024 Tang et al. 2022). However, prevalent AR models flatten images ID sequences of tokens in row-major raster-scan order. While it aligns with the sequential nature of language, it overlooks the inherent 2D structure of images, where each token exhibits strong relationships with its neighbors. This straightforward adaptation significantly limits the capabilities and further development of AR models.
Recognizing these limitations, recent research (Fan al. 2024 Li et al., 2024b Yu al. 2024c Li al. 2025: Pang et al., 2024) explores alternative strategies to suit the characteristics of images within the AR Tramework. VAR (Tian et al., 2024) moves from the standard next-token predic- tion to the coarse-to to-nee next-scale prediction. MAR (Li et al. 2024b) transforms the traditionally causal, unidirectional generation into a bidirectional attention mechanism. Simultaneously, other explorations (Ren et al. 2025 Yu et al. 2024b Wang et al. 2024 Yu et al. (025) also investigate various aspects such as flexible token definitions, randomized generation orders, parallel processing, and Trequency-based generation address the inherent challenges of AR models.
However, these advancements are hindered by two fundamental challenges. First, they rely heavily on manual designs and inductive biases. VAR (Tian et al.) 2024) is based on the coarse-to-fine causality inspired by human perception, FAR (Yu et al., 2025) opts to exploit
sisquency-domanl hierarchy, while xAR (Ren et al. 2025) directly groups adjacent tokens as cells. These ad hoc choices yield divergent conclusions from their own inductive biases. Second, these approaches lack unified mathematical framework and formal foundations, undermining their credibility and

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Published as a conference paper at ICLR 2026
persuasiveness. For instance, PAR Wang et al. 2024) partitions tokens by their locations, RAR Yu et al. 2024b) randomly permutes tokens and gradually anneals to normal order, and xAR (Ren et al.
2025 empirically adopts cell as the basic entity.
To address these gaps, we propose Basis Autoregressive (BAR), including two pivotal contributions, e.g. unified mathematical framework and parameterized learnable algorithm. First, our frame- work is grounded in the theory of linear spaces and formalizes prior AR variants (Tian et al. 2024]
Ren al. 2025; Yu et al. [2224b] Wang al. 2024 Yu al., (025) as specific transforms of space. They essentially re-mix, re-order, and re-group the token sequences with manually defined rules, while our framework is compatible with them and further offers generalized viewpoint. Second, leveraging this framework, we introduce parameterized, learnable, and end-to-end optimization algorithm that does not rely on heuristic designs and human biases. This avoids reliance on hand- crafted priors, eliminates extensive experimental trial and errors, and allows the model to adaptively discover optimal transforms through training.
As visualized in fig. 1 we first partition the latent space of token sequences x into series of sub- spaces, where each token zi is the projection on them. Then, we apply the linear transform y Ax, and the row vectors of A form the basis of transformed space. Prior methods (Tian et al. 2024 Ren jet al. 2025 Yu et al. 2024b; Wang et al. 2024 Yu et al. 2025) are exemplified as certain forms of A. Then, propose a joint learning algorithm in fig. for the matrix with the training objectives derived from existing AR models. Our method enables end-to-end training that seamlessly integrates with them and is firmly supported by comprehensive experiments conditional and text-to-image generation, profound ablations of the learned transform matrix, and the state-of-the-a FID score of 1.15 on ImageNet 256 benchmark. Our contributions are:
A unified framework that formalizes former AR methods and facilitates novel extensions;
An end-to-end learnable algorithm that transcends human biases into adaptive optimization;
Comprehensive experiments and ablations underscore the advantages of our method.
2 BACKGROUND
2.1 DISCRETE AUTOREGRESSIVE VISUAL GENERATION
Autoregressive (AR) models for visual generation adapt the paradigm of sequential modeling from the field of language. primarily through discrete tokenization. While early approaches (Van den Oord et al., 2016 Van Den Oord al., (016) directly model pixel-level dependencies, VQ- VAE (Van Den Oord et al. 2017] Razavi et al. 2019) introduces vector quantization and maps images to discrete tokens. Later works (Ramesh et al. 2021 Yu et al.] (002) scale text-to- image generation, demonstrating the potential of AR. LlamaGen (Sun et al. 2024) further adapts large language model architectures, egg. Llama (Touvron et al. 2023). Given sequential tokens x {21, . .NN] representing an image, AR assumes that each token I depends only on its prefix T<c := {x1, #2 ... 1k and factorizes the joint distribution px(x) into a product of conditioned probabilities over the sequence as (x(x) = -I Po I<()).
Recent advancements focus optimizing token quantization, prediction, and efficiency. RQ- introduced residual quantization to reduce codebook redundancy.
Transformer (Lee et al. 2022)
reduces the number of required tokens encode image down pioneered a coarse-to-fine next-scale prediction paradigm, using a VAE to generate tokens at increasing resolutions. PAR (Wang et al. 2024) introduces parallel decoding by identifying weakly dependent tokens as groups RAR (Yu et al. 2024b) addresses fixed factorization orders via randomized permutations, gradually anneals to nor- mal orders during training, and learns bidirectional contexts of images.
while TYTok YYu al.
2024c)
to 32. VAR (Tian et al.
2024)
custom multi-scale RQ-VAE
2.2 CONTINUOUS AUTOREGRESSIVE VISUAL GENERATION
Continuous AR models bypass vector quantization to directly model high-fidelity visual contents. Hybrid approaches (Zhou et al. 2024 Xie et al.] 2024) attempt to bridge discrete and continuous visual data with multi-modaa models. Later, MAR (Li et al. 2024b) eliminated vector quantization by integrating a diffusion loss, where the output tokens of AR are fed into tiny denoising networks conditions generate continuous outputs. Specifically, the output of AR models, noted 2k, no
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(00 linear truns
Ax
(C) Auturr Auturggrossee moddling difiorest transfomm
>/2
1/2
y/3
34
Y/S
AB
42
(6) Tokento gro prosetion sottone beock
y
Y22
y/=
42
y== y/1
Figure 1: An overview of the unified framework of BAR and its strength over previous approaches. (a) By applying a linear transform associated with the matrix A, BAR offers the generalized view- point that encompasses prior methods as specific instances of A and facilitates further extensions. (b) BAR at its core lies that each token 2y is the projection of whole image x on a sub-space, or basis with channels omitted. It transforms the standard basis ej into the row vectors aj of matrix A. (c) We illustrate each method with its corresponding dg. While vanilla AR directly employs e; as raster of tokens and VAR manually designs coarse-to-fine pattern, BAR adaptively learns dg-
longer matches the image tokens and serves as the condition for the noisy estimator Ep. The noisy estimator is trained via denoising criterion
LMAR (Fx, mTne = - =x)1
(1)
where e ~ (O, 1) is random noise, o = VaLza + /I āge is the noise-corrupted sample, and is the noise schedule. Following works like FAR (Yu et al. 2025) in turn adopted frequency- domain strategy, generating low-to-high frequency components to align with visual hierarchies, and captures spatial dependencies efficiently. Furthermore, xAR (Ren et al. 2025) eliminates the diffu- sion heads of MAR, drives the decoder to directly predict the continuous tokens, and uses groups of local tokens, e.g. cell, as the unit of each AR step. xAR also utilizes the flow-based (Lipman al. 2023
Liu el al. 2023) objective
(x) =
Avo(aaf100 ..... 5 #=1
da 1 },4+) u/k 1//112
te dzf
where 2 = (1 tx) tx) - + f4CC is the noisy sample, uk dta
cx xx is the ground-truth flow,
{t) = (2,, )n) U(0, 1] are timesteps, and {e} {ci, ..... en) N(00 1) are noise.
METHOD
3.1 UNIFIED FRAMEWORK
Consider an image encoded into a 2D feature grid {x(1,)) where each element corresponds to a K.....,K] K} in the case of
local patch of image, I(iij) E Rd in the case of VAE, and ((.j) E ΣK == {I,..., VQ-VAE. AR flattens it into a ID sequence of tokens x = (Ii, 22,,,,,,..... INN) The entire image can also be viewed as vector x R.N xd or x Z for continuous and discrete cases, respectively. AR transforms the modeling of the whole image into the progressive predictions of each token Ik. which can be viewed as the projection from the high-dimensional x yielding series of low- dimensional in different sub-spaces. In the following discussion, we omit the channel dimension for simplicity, since the transform can be independently applied on each channel.
Specifically, consider the standard basis {e1, . eN of S = N where e onehot(k) E R with its k-th element being one and others being zeros. AR splits the S into the sub-spaces
(S (pan(ex), < N),
(3)
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where span(e+) represents the space spanned by cj. AR transforms the direct modeling of into progressively determining its projections onto Sk, e.g. each token Ij- However, specific designs of these sub-spaces {S&] remain understudied, most AR models simply adopt the vanilla form above that corresponds to the row-major raster-scan of image patches.
Therefore, propose the next-basis prediction paradigm and Basis Autoregressive (BAR) mod- els with a linear transform operation that multiplies the image vector x by a full-rank matrix and transforms it to another space S' == R.N'
y == Ax,
(4)
where y = [y1, U2.............................. " E S' and A = {ai ag..... .... E N'N, The row vectors of A, e.g. ax R., form the basis set of S'. Consequently, BAR projects y onto the sub-spaces
S sp)n(a)), 1 S k N
(5)
and progressively predicts yk. e.g. the projections onto each sub-space Sy. We apply standard AR models on new sequence y. following with reverse transform x = - back to the original space S. BAR refactors the standard basis and sub-spaces {Sx} of vanilla AR into the transformed basis and sub-spaces {S)). This linear transform serves as a unified framework that allows to incorporate and generalize previous methods as different designs of the transform matrix A.
3.2 SPECIAL CASES
While previous methods also propose transform the image token sequences, they predominantly rely on human inductive bias and lack rigorous mathematical formulations. xAR introduces a next- X prediction paradigm where X can be instantiated token, subsample, and scale. However, the concept remains a textual description and xAR empirically adopts cell, egg. a group of adjacent tokens, as the basic unit. Here, we systematically discuss prior works special cases of matrix A.
VAR TTia et al. 2024) leverages a coarse-to-fine strategy of next-scale prediction, which can be viewed mulii-scale transform A with its basis og the average pooling of different resolutions. The sequence y thereby reflects the progression from global features to finer local details.
xAR (Ren et al. 2025) groups grid of spatially adjacent tokens as cells and sequentially predicts them. In this case, A also represents the re-ordering and re-grouping of the standard basis set {ex}, where 6₁ and e are grouped together if æg and ø are spatially adjacent on the 2D feature grid.
RAR YYu et al.) 2024b) randomly permutes the token sequence during training, and gradually anneal normal. The matrix A is thereby random permutation matrix P, and gradually anneals
PAR (Wang et al. 2024) accelerates inference by predicting groups of tokens with weak dependen- cies, e.g. sub-sample, in parallel. Here, the transform matrix A takes specific form of selection where with its corresponding 24 in the same sub-sample placed together.
FAR Yuu al. 2025) performs AR in the frequency domain, instead of the spatial domain, from low-frequency to high-frequency components. Similarly, the transform matrix A can be constructed as multi-frequency filters, where each dg is low-pass filter with different cut-off frequencies.
TiTok YYu et al., 2024c) is designed to tokenize an image into an ultra-compact 1D sequence of M & latent representations. The corresponding transform matrix A E IR MN serves as an abstraction from the long sequence E Nx xd into the short sequence
Rdxxdd
FractalGen (Li et al.) 2025) proposes the AR modeling with recursive, self-similar architectures inspired by fractals. The corresponding matrix A would be similar to VAR with its basis dg repre- senting hierarchical structures, generating the sequence ys at various levels of the fractal recursion.
3.3 LEARNABLE APPROACH
Prior AR models, as discussed above, often depend on static hand-crafted designs of specific pre- diction units orders derived from inductive biases. and might lead to divergent conclusions based on similar empirical observations. Therefore, we propose an adaptive algorithm to parameterize and learn the transform matrix A in end-to-end manner alongside the AR model itself.
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Ax
Comdition (label, text)
Couu lly
911
reedaa
xx A'91
1/1
Trannffurmer
dy
Y's
y5
Figure 2: Pipeline of BAR and our learnable approach of transform matrix As. The transform matrix A learnable parameter is end-to-end optimized along with AR transformer. While LAR effectively trains BAR models, we further apply Lresidual BAR to encourage ordered
We narrow the search space for the transform matrix A to enhance efficiency without loss of gen- erality. Firstly, we follow prior methods to omit the channel dimension and treat each token whole, as AR typically progresses on the sequence dimension. Secondly, we consider A E RN be square matrix, as it does change sequence lengths and remains minimum modification of existing AR models. The matrix A essentially exchanges the standard basis {ex } for learned basis {ax}. Furthermore, we focus on the orthogonal matrices, a noteworthy category for the transform matrix A, in this work. Such matrices possess desirable properties for learnable approach, for example, they preserve the Euclidean norm of vectors, e.g. lylle ||x|| where y Ax.
To facilitate the adaptive search for the transform matrix A, treat it learnable parameter along with AR models and derive a training objective equivalent to previous AR methods. Here we mainly focus continuous AR models. We have the following proposition.
Proposition 1. Optimizing BAR on the transformed image y and token sequence (yk is equivalent MAR on the original image x and token sequence {I i.e. EMAR(ZN,, 9R) LMAR (2MA (2))
Proof. Consider reference model optimized with LMAR, we rewrite eq. ①
Cref (x) = Σ cx - en (1 20(x=<x))11
V Vo
(ak
(z)
vI a(c
2
(6)
V1 α
Vār
Vār
N Σ
(Ix
xx))
āi [[x - x)11
1
2
where ds. vor (at - -4Gy) is obtained via the reparameterization of the noise prediction en, and is the predicted image vector. the other hand, we also apply MAR our transformed sequence y Ax. The correspondents of noisy tokens æf in the transformed space S' are
N
v = oh
x
Σ
and (Vorn + v1 -1451)
1=1
N
N
/
+
VI
Oe
ag.efr = Vārya + vI - are
1-1
where e ;= Dm de is the transformed noise. Note that if we denote e = {EI, E2, En and
o' == (66,6/ (c.,, ,.., we have e' As. Els') AB((s) 0, and Σ. EE[(s' E(e'))
B(s')) (A() which suggests that e' is also composed of i.i.d. Gaussian noise.
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The subsequent BAR objective on the transformed image y is
LBAR(Y)
Σ
1k
=0,
=o(
N
v a
(8)
(yxx - 8Kc)
l1yy
-2
k=1
0t
2
1 āi
||A( x))1
MAR
ai
which indicates that optimizing BAR on y is equivalent to optimizing the underlying MAR on x.
Proposition 2. Optimizing BAR on the transformed image y and token sequence {yr} is equivalent to xAR on the original image and token sequence {zk}, i.e. LBAR(y) = (x).
also train xAR models the transformed image y and token sequence {yx } and leave the detailed proof for the following proposition in the Appendix. The propositions and 2 ensure that LAAR is valid objective as LMAR and LAAR. egg. the performance of BAR and MAR(xAR) would be the same when optimizing only the network parameters. However, when incorporating the learnable matrix A, we will see great improvements in the following experiments.
Similarly,
3.4 RESIDUAL OBJECTIVE
While propositions and indicate the potential for direct optimization of the transform matrix A, the full exploitation of the capabilities of AR models necessitates the incorporation of certain desirable properties. Specifically, a primary objective is the maximization of information content within the earlier basis vectors dg. This aims to facilitate the most accurate possible reconstruction of the image x utilizing earlier tokens yk. a characteristic intrinsic to the sequential token prediction introduce residual training objective designed to explicitly
nature of AR models. Consequently, enforce an ordering of the basis vectors ag and tokens yı according to their respective information richness and their contribution the image recovery process.
Note that the BAR objective in eq.
(8) can be rewritten as
CBAR (y) = 1 αe we propose the residual BAR objective as
ā; ||y 212
āc
||A - AT
āt 1- αi
||- A
T3
(9)
1 ai
N Σ
Cresiduall (eRssdaaBBBR())) (y) =
Ot
x
A
Fxll2 where 5k = 8 T
el).
(10)
Cte
1=1
Here, Yk is the k-prefix of y, i.e. fk == (51, ..,,.., ØN where Je D1 for S S and ÿi for is < N. The motivation lies that the first output token y1 should maximize the recovery of image and the following tokens y should maximize the recovery of the residuals x A Yk-1-
Discussion Cresidual BAR partially shares the same principle as VAR and RQ-VAE. While VAR sumes the average of patches coarse contexts and RQ- VAE progressively quantizes the remaining residuals, our design enables an adaptive learning process and introduces fewer inductive biases.
3.5 IMPLEMENTATION DETAILS
Regularization is critical to our learnable algorithm, since we assume A to be orthogonal. Specifi- cally, the term Zreg A A I and train models with LBAR Lreg or Cresidual BAR Lre--
Orthogonal projection as closed-form solution of Orthogonal Procrustes problem (Schönemann 1966 Ge et al. 2013) applies Singular Value Decomposition (SVD) as USVT = A, then lets A US, where the diagonals of S is clamped to (1 8, 1 + 8) as S, with 5 = 0 in hard projection and (0, 1) in soft projection.

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T4X
239
253
FFHQ (Pie spacc)
:
106
187
249
FPHQ (Tatent sper)
O COC
198
253
ImageNet (Late spocs)
Figure 3: Visualization of learned basis ag with & denoted above. Darker marks higher values.
Table I: Benchmarking conditional image generation on ImageNet 256 256.
Type
Model
FID
1St
Pre.t
Rec.t
Timel
#Stepl
#Param.
Diff.
ADM
Dhariwal & Nichol 2021
4.59
186.7
0.82
0.52
44.68
250
544M
Diff.
LDM (Kombach et al.
2022
3.60
247.7
0.87
0.48
207.2
250
400M
Diff.
U-VIT [Ba at. 2023
2.29
263.9
0.82
0.57
501M
Diff.
DiT (Pechles Xie 2023
2.27
278.2
0.83
0.57
11.97
250
675M
Diff.
Ma al. 2024
2.06
277.5
0.83
0.59
11.97
675M
Diff.
VDM++ [Kingma Gao
2023
2.12
267.7
0.81
0.65
2.0B
Diff.
MDTv2 Gao el 2023
1.58
314.7
0.79
0.65
250
676M
Diff.
REPA Yu et al. 2024d
1.42
305.7
0.80
0.65
11.97
250
675M
Diff.
Light
Yao & Wang
2025
1.35
295.3
0.79
0.65
250
675M
Diff.
MG [Tang ct al. 2025
1.34
321.5
0.81
0.65
6.03
250
675M
Mask.
MaskGIT (Chang et al.
2022
6.18
182.1
0.80
0.51
0.5
227M
Mask.
RCG (Li al. 2024a
3.49
215.5
1.9
20
502M
Mask.
TYTok ef al. 20246
1.97
281.8
64
287M
AR
VOGAN EEser al.
2021
5.20
280.3
6.38
1.4B
AR
RQTrans, (Lee et al.
2022
3.80
323.7
3.8B
AR
FAR Yu el al. 2025
3.21
300.6
0.81
0.55
10
812M
AR
PAR (Wang ct all 2024
2.29
255.5
0.82
0.58
3.46
147
3.1B
AR
LlamaGen (Sun et al. 2224
2.18
263.3
0.81
0.58
12.41
576
3.IB
AR
VAR (Tian al. 2024
1.73
350.2
0.82
0.60
0.27
10
2.0B
AR
FlowAR [Ren el
2024
1.65
296.5
0.83
0.60
10
1.9B
AR
MAR [L al. 20246
1.55
303.7
0.81
0.62
28.24
943M
AR
RAR Yu al.
2024b
326.0
0.80
0.63
1.5B
AR
XAR (een al.
2025
1.24
301.6
0.83
0.64
1.1B
AR
BAR-B(ourr)
1.56
292.4
0.83
0.63
0.08
50
172M
AR
BAR-L ((o-s))
1.21
301_1
0.84
0.64
0.27
608M
AR
(AR-H(
1.15
327.1
0.86
0.68
0.68
1.1B
Initialization of the transform matrix A is important for its optimization. While the identity matrix I corresponds to vanilla AR, we can also use a random matrix followed by an orthogonal projection.
4 EXPERIMENT
4.1 SETUP
Implementation. We apply our BAR framework to two different architectures of AR and follow the protocol in MAR (Li et al. 2024b) and xAR (Ren et al.] 2025). We primarily conduct experiments on the ImageNet (Deng et al. 2009) 256 256 dataset and then raise the spatial resolution of images to 512 x 512. We also conduct ablation studies on the FFHQ (Karras et al. 2019) dataset for its human- www.-aacceeeeeeeeeeeeeeeeeeaee-e
nature at 64 x 64 and 256 x 256 resolutions. The KL-16 continuous tokenizer provided by LDM (Rombach et al.) 2022 is employed to encode the images into latent tokens. Our models are mainly based on xAR (Ren et al. 2025). and we conduct ablation experiments with
XAR-B. All models trained following previous settings (Li al. 2024b) Ren al. 2025). e.g.

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FTTQ
ImugeNet
Figure 4: We decode the generated sequences every 25 tokens. The first column uses only token.
Figure 5: Uncurated samples on ImageNet 256.
Figure 6: Generated text-to text-to-image samples.
800 epochs and the batch size of 256, for fair comparisons, and all experiments are conducted with 16 NVIDIA A100 40G GPUs. For the text-to-image generation task, we follow FAR Yuu et al. 2025) and use the JourneyDB (Sun et al. 2023) dataset and the Qwen2-1.5B (Yang et al. 2024) text encoder.
Evaluation. As metrics, report the commonly adopted Frechet inception distance (FID) (Heusel ct al.] (017). Inception Score (IS) (Salimans et al., (2166). Precision (Pre.), and Recall (Rec.) (Kynkäänniemí al. 2019)
50K generated samples, which is consistent with previous works. We also list the number parameters, sampling steps, and the wall-clock time to generate one image for each method, which facilitate the thorough investigation of the balance between sam- pling quality and generation efficiency. For the text-to-image generation task, we follow FAR (Yu measure FID-30K on MS-COCO 2014 (Lin al. 2014) and the GenEval (Ghosh benchmark.
al.
2025)
et al.
2023
4.2
MAIN RESULTS
ImageNet 256 x 256 benchmark. In table we present the system-level comparison of conditional generation performance on the ImageNet 256 x 256 dataset with concurrent advanced methods, including diffusion, mask-based, and AR models. Notably, we achieve new state-of-the-as results with an FID of 1.15, while our BAR-B model also exhibits strong performance with only 172M parameters and a lightning speed of 0.08 seconds per image. While our models offer outstanding generation quality, they also faster than most of the previous methods. The generated images of our model are provided 5
Compatibility with different architectures. While our models are mainly based xAR, show in table 2 that the framework of BAR is also compatible with other existing AR models. We additionally apply method to MAR and experiment with their -B, -L, and -H variants. The significant improvement over their corresponding baselines indicates the effectiveness of BAR on different AR approaches and model sizes.
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Table 2: Experiments on different models.
Table 4: Experiments on text-to-image.
Model
FID
ISt
Pre.t
Rec.t
Model
FID
GenEvalf
MAR-B Lietal 2024b
2.31
281.7
0.82
0.57
LDM Rombach et al.
2022
12.70
0.37
+ +BAR
2.18
289.6
0.83
0.60
LlamaCien (Sun el a.
2024
15.05
0.32
MAR-L (Li al. 2024b
1.78
296.0
0.81
0.60
FAR et 2025
13.91
0.37
+BAR
1.56
304.1
0.83
0.61
BAR
12.55
0.39
MAR-H (Li ct
2024b
1.55
303.7
0.81
0.62
Table 5: Ablation on initialization.
+BAR
1.49
312.8
0.82
0.64
XAR-B (Ren et al. +BAR
2025
1.72
280.4
0.82
0.59
Initialize
FIDI
ISt
Pre.
Rec.
1.63
291.3
0.83
0.62
Baseline
1.72
280.4
0.82
0.59
XAR-L (Ren et +BARigus
2025
1.28
292.5
0.82
0.62
Identity
1.63
291.3
0.83
0.62
1.24
299.7
0.84
0.64
Orthogonal
1.66
289.6
0.83
0.61
XAR-H [Re et ul.
2025
1.24
301.6
0.83
0.64
Table 6: Ablation on orthogonal projection.
+BAR
1.15
324.5
0.85
Projection
FID
1st
Pre.
Rec.t
Table 3: Experiments on ImageNet 512.
Baseline
1.72
280.4
11.82
0.59
None
1.70
264.9
0.81
0.61
Model
FID
ISt
Pre.t
Rec.
Hard
1.66
285.8
0.82
0.61
VAR
Tian al. 2024
2.63
303.2
0.82
0.62
Softs=o.s
1.63
291.3
0.83
0.62
REPA
Yu al.
2024r
2.08
274.6
0.81
0.61
EDM2
Karras et a.g 2024
1.81
273.2
0.85
0.63
Table 7: Ablation on training objective.
MAR-L
et
2024b
1.73
279.9
0.84
0.62
Objective
FIDI
1St
Pre.t
Rec.t
+BAR
1.65
287.7
0.85
0.64
Baseline
1.72
280.4
0.82
0.59
XAR-L RRen et al. 2025
1.70
281.5
0.84
0.64
CBAR
1.64
289.7
0.84
0.64
+BAR
1.63
292.0
0.85
0.64
Cresstual
1.63
291.3
0.83
0.62
Scalability to ImageNet 512 x 512. The extension of our method to high-resolution images is
also notable. We conduct experiments on the ImageNet 512 x 512 dataset in table 3 and the markable margin over both MAR and xAR baselines demonstrates that BAR is capable of modeling challenging distributions and longer token sequences.
Text-to-image generation. In addition to the condiioondt task on ImageNet, we also employ BAR for text-to-image generation and depict the comparison in table Following FAR (Yu et al.) 2025), our model further surpasses it by a gain of 1.36 FID. It suggests that BAR is promising across various conditioning modalities. We also present the generated samples of our method in fig. 6
4.3 ABLATION STUDY
Visualizing learned basis. We visualize the learned basis og in fig. where k is denoted above each subfigure. The basis og is reshaped to match the 2D feature grid of images, and darker regions mark high values, Lee. the weight of corresponding image patch is higher for ag. Here, we additionally experiment on pixel-space 64 x 64 FFHQ and patchify 4 x 4 pixels as a token. The basis on pixel- space FFHQ clearly reflects the shape of human faces, while the basis on latent-space FFHQ exhibits less continuity, which explains the success of AR models on tokenized images. Furthermore, the earlier basis on ImageNet shows an interesting pattern, while later ones seem to be more random, which is beyond static hand-crafted designs.
Visualizing generation process. We also visualize the generation process of BAR models by pro- gressively decoding the generated token sequence with its prefix, e.g. we only decode the first k tokens with i increasing with a step size of 25 starting from the first token. The output images also show coarse-to-fine paradigm, which is consistent with the motivation of our residual objective.
Initialization strategy. The initialization transform matrix A is critical to our learnable approach. In 5a using the identity matrix I as initialization obtains using best results, since it corresponds to vanilla AR models, while our method also offers a gain over the bascline with random orthogonal initialization.
Orthogonal projection. The orthogonal projection is also crucial to the training process. In table 6 the soft projection with 5 = 0.5 offers the best results, while the performance is significantly im- paired without projection. The main reason is that the regularization term for orthogonality alone is not strong enough, while hard projection limits the potential update directions for A.
Training objective. Although LAAR itself is capable of effectively training BAR models, we further introduce and apply Fresidual BAR that encourages ag be ordered by the recovery of the original

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Published as a conference paper at ICLR 2026
images and mimics coarse-to-fie characteristic in fig. 4 The results in table confirm that both LAAR and Lesiduul BAR provide satisfactory performance, while Cresidual BAR is slightly better.
5 CONCLUSION
In conclusion, this work introduces Basis Autoregressive (BAR), novel paradigm for image gen- eration that addresses the inherent limitations of traditional AR models tied to fixed, raster-scan prediction of tokens. By conceptualizing tokens as the projection image vector on basis of lin- space and employing an end-to-end learnable transform of these bases, BAR offers unified mathematical framework. It not only encompasses previous methodologies as specific instances but also adaptively optimizes the transform to discover effective strategies beyond manual designs. The demonstrated state-of-the-art performance, highlighted by an FID score of 1.15 on the ImageNet- 256 benchmark, underscores its capability to transcend human biases and significantly advance the field of image generation, including its application in text-to-ine rext-to-image synthesis. BAR represents significant step in developing more flexible and powerful AR models for visual content creation.
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A PROOFS
A.1 MAR VARIANTS
In this section, we provide further details of propositions I and and their corresponding proofs. We first begin with BAR implemented with existing MAR architectures.
Proposition 1. Optimizing BAR the transformed image y and taken sequence {yk is equivalent to MAR on the original image x and token sequence (#k), i.e. LMAR(ZE, Us)
Proof. Consider reference model optimized with LMAR- Recall that the noise-corrupted sample obtained via the interpolating ground-truth image and sampled noise via the noise schedule
x = Vr + vI Og,,
(11)
where e ~ (0, 1) is random noise drawn from Gaussian distribution, and á is the noise schedule used in diffusion models (Song & Ermon 2019 Ho et al. 2020). Given the model outputs predic- tions of added noises, we can obtain the prediction of unnoised image & via the reparameterization
āzé
f
where é:= e =T(x))))
(12)
Va
We thereby rewrite eq.
T as
N
CTe (x) =
Σ
c1: - (2fft,, 20(1=2))111
k=1
(VI Ciek vI agtnn) v1-dmen)
α2
2
(11) v1 -iee)) - (x/ - v1 (rten)
12
(13)
V1 00
(at v1 - a(ck)
(2t - v1 Ō)6E))
12
at
Vax
Vāa
(Ix
xxk)
Ot
[|x
x 1|
On the other hand, we also apply MAR to our transformed sequence y = Ax. The correspondents of noisy tokens of in the transformed space S' are
0 x
Σ akd (Vāg + vI a(E)
(14)
N
Vol
11 + vI a4
1
Voigh
+ +VI -asE
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where the noise added to transformed tokens yk is
(15)
Note that if we concatenate all noises into single vector and denote == {ei, .......: CN and := .,....,.y we find that first sampling E ~ (N(0,, 1) then using the transform in eq. 15
i.e. = Aε, to obtain equivalent to directly sampling from ~ (O, 1). To validate this, we can calculate the expectation of g'
E(c') = -B(A)) = (E(e) = 0,
(16)
and its covariance
Σg El(s' - B(s'))( T
E
-AE(A
TR(AEE A
A TJAT
(17)
ABI(E B(e))(E -AA
AT
AAT
= I,
which suggest that e' is also composed of i.i.d. Gaussian noise and can be directly sampled with ~ No 1). This ensures that we can directly apply MAR framework on the transformed image y. The subsequent BAR objective is
LBAR (y)
Σ
11c6
< =0(==))))<)))
2
Σ
(VI - -aré - -II
vI a
12
Σ
(uv - (1-rrcc) - (ui v1 -r(c,)
v1 az
N
Va
(v
VI-areh
(vk vI VI- (reE))
12
Vou
(18)
2
(yx 2x
α2
2
(ly - 8)11
di
| (x - x)112
d+
||(x - x) 2
de.
MAR:
which indicates that optimizing BAR on y is equivalent optimizing the underlying MAR 17
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A.2 XAR VARIANTS
Then, discuss the case where BAR is implemented with the model architectures of xAR. and provide the detailed proof of proposition 2
Proposition 2. Optimizing BAR on the transformed image y and token sequence {yk) is equivalent to xAR on the original image x and token sequence {zx}, ie. LBAR(Y) = (x)
Proof. Consider reference model optimized with LAAR Recall that the noise-corrupted sample is obtained via the interpolating ground-truth image and sampled noise by
* (1 tx Jo + tgEk:
(19)
where Eg (O 1) Gaussian noise, and the ground-trute -ruth flow is
dat
k
ft
dl
(20)
Similarly, we can obtain the prediction unnoised image via the reparameterization
Cl=
where
tt :=:o vo((2t ...,....,, ).t)..
(21)
We thereby rewrite eq. as
Juo (ot 22.2 ...., xx do },tx) 2//
XAR
N
l1(c= - =xx) - (cx 2x)112
(22)
k=1
N
|
=xx12
*
x|2
On the other hand, also apply xAR to transformed sequence y Ax. The correspondents of noisy tokens of in the transformed space S' are
af x
Σ ax
N
axe7 ((1 - 4))z + (16))
(23)
1=1
(1
tx) Σ
a + t
1=1
I=1
(1 tx)yk= + t2
where assume that Vi (1,2....,k, k) and {1, 2........ k),, 4 1, for simplicity, since {!}
(4,,22.... (n,....,, ~ U(0, 1] is arbitrarily sampled in xAR (Ren et al. 2025). The noise added to transformed tokens yk is
ag
(24)
Note that if concatenate all noises into single vector and denote {e1, 62, . En and
: (c...,..... Jy., we find that first sampling E g~ NO, 1) then using the transform in eq. 24).
i.e. e' = As, obtain s' is equivalent to directly sampling from s' ~ ~N, 1). To validate this,
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calculate the expectation of and its covariance
EEE') B(AE) AB(E)
(25)
0,
E. E[(E' -
El''E'T
[A((A
IE[AEE A
ABEEE AAT
(26)
ABI(E B(E)) (e)))e-B(e))]]) BA
AT
AAT I,
which suggest that e' is also composed of i.i.d. Gaussian noise and can be directly sampled with E' (0, 1). This ensures that we can directly apply xAR framework on the transformed image y.
The subsequent BAR objective is
LBAR
Σ polluu v/.3. ....,.% 3.
b.tx) ./.
Ae 1
I1(c (1c) (c2 yx)11
Σ 11 yk 12
(27)
k=1
|| y11
||A (& - x)1
||* x12
Cref
where the ground truth flow of d is
delk dlx
c - yk.
(28)
B LIMITATIONS AND BROADER IMPACTS
Limitations This work focuses on enhancing the output quality and training speed current AR models, but still depends existing VAEs (Rombach et al.) (022). Recent studies (Yao & Wang. 2025 Leng al. 2025) achieved significant success with the end-to-end training of VAE and AR models, and incorporating this work are mainly conducted on continuous AR models. Extending BAR to discrete AR models an imperative next-step,
approach into VAE would be promising direction. Furthermore,
discussed in section E
Broader Impacts Although this work primarily discussed images generation AR models, the next- token prediction paradigm is employed other modalities, e.g. video and speech. Applying this work to AR models in these fields shows potential. On the downside, since our models are trained on existing dataset, it might unintentionally reproduce any biases within. Furthermore, the image
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generation abilities developed could potentially be misused to create and spread false information. We will consider restricting the access to our model weights to address this.
Table 8: Setup for table
BAR
Archilecture
Takenizer
(Rombach
Rombach
(Romhach
Inpui dimension
16X
10:10
Encoder layers
16
200
Encrder dimansion
768
1074
1250
Encoder heads
16
16
Decoder layers
16
20
Decuder dimsension
768
1024
1280
heads
parametens
Hyperparameters
Optinizer
Adaon Kingms
Loshchilov 3019
Adamn (Kingms 20144 Loscchilov 2019)
Kiagms Loshchilor
Momentum (5t,)32)
03900000
(0.3) 0096)
(03)
Weight decay
0,02
0102
0.002
Ratch sine
2048
2048
2048
Learning rate schedule
cusine
cosine 10-*
cusine
Peak learning
100-
x 10-4
leaming
100-5
10-0
10-5
Tosal epects
Wammup spachs
Dropout rale
0.1
Label dropout mic
0.1
0.1
0.1
Inference
Sampler
Foler- Fuler-Mennyam
Fules Monnams
Fule-Mamiyam 50
Steps
50
50
Algorithm Training BAR: PyTorch-like Pseudo-code
def train (residualillllseeeoo ("assiduallllss--rruee
for step, (x, c} in enunerate (data adataloader) oader)
# sample random noise and timestep noise - forch.randoe (x, shape) timestep - torch. rand (x. [0], 1, 1)
# BAR: linear transform y x 0 mett.A_mat
sample y-t from
y_t = (1 timestep)
+ timestep noise
predict v vat and y yat from y_t
wat net (y_t, timestep, c)
yahat - noise vat
compute loss
if rest dua 1_soss:
hat = [y_batl:.. k+]] @ self.A_matli, sk+1] for k in range (x.
shape[-1]]]
loss (ttorch.stack hat, dim=1) x.unsqueeze (1)) mean
elae:
loss (ty_hat. y) ** 2) m)
regularize term
loss += ((self.A self.A Self.Ammt mat.r .I torch. (self. mat shwpe (01))
** mean
optimize opt opt.step()
opt gpt.zezo_grad
C HYPERPARAMETER AND IMPLEMENTATION DETAILS
Implementations. We implement our method based on the code of xAR (Ren et al. 2025 and MAR L et al. 2024b). We use the exact same structure and same hyper-parameters as xAR (Ren et al. 2025) and MAR (Li et al. 2024b) throughout all experiments. We use batch size of 2048 in consistence with xAR (Ren et al. 2025) and MAR (Li et al.) 2024b). and we apologize for the typo in the main text of the batch size of 256. We AdamW (Kingma 2014 Loshchilov 2019)
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with cosine learning rate schedule starting from 4 x 10-4, warm up for 100 epochs, and gradually decay to x 10 The optimizer momentum (31, (2) = (0.9, 0.96) and the weight decay is 0.02. We also pre-compute and save the latent vectors of images and these latent vectors for training, similar to xAR (Ren et al. 2025) and MAR (Li et al. 2024b). Therefore, we only apply simple random horizontal flip data augmentation. We use continuous KL.-16 VAE from LDM (Rombach) et al. 2022) for encoding and decoding images. The detailed hyper-parameter setup are provided in table
Sampler. For MAR variants, we use the ADM (Dhariwal & Nichol, 2021) sampler with 100 steps the same the original MAR (Li al., 2024b). For xAR variants, we use the Marler-aaryyama sampler (Ma et al. 2024 Yu et al. 2024d) with 50 steps the same as the original xAR (Ren et al. 2025).
Computing resources. We use 16x NVIDIA A100 40GB GPUs for experiments. We use batch size of 2048 and remain unchanged for all experiments.
Pseudo-code. We provide torch-like pseudo-code of training models with BAR in algorithm
D TRAINING WALL-TIME AND EFFICIENCY
D.1
CONVERGENCE SPEEDUP
50
xAR
BAR
40
FID-5K
30
20
10
0
100
200
300
400
Epochs
Figure 7: We train BAR-B and xAR-B for 400 epochs. Our BAR-B converges significantly faster than xAR-B, and obtains lower FID-5K throughout the whole training process.
BAR not only improves the final generation quality of AR models, but also accelerates the training process and its convergence, since the image tokens are transformed and refactored to better suit the nature of the next-token prediction paradigm. As illustrated in figs. 3 and 4 the basis and transformed tokens mimic coarse-to-fin pattern, allowing the AR models first focus the global structures then refine the local details.
In fig. conduct ablation experiment with BAR-B model and compare the intermediate FID-5K evaluation results with xAR-B during the training process. As shown, the convergence speed of BAR is significantly faster than xAR, and our BAR-B model obtains better performance compared to xAR-B under the same iterations throughout the whole training process.
D.2 TRAINING EFFICIENCY
We also compare the wall-time per iteration and GPU memory usage during training in table using one A100 GPU. Since BAR only introduces an additional matrix multiplication the training process (see algorithm both the training time and memory cost of BAR is the same the original xAR. When incorporating the proposed residual loss to explicitly regularize the order within learn basis, the training cost is slightly raised by the overheads of 0.01 x wall-time and x.03 memory.
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Table Training efficiency of BAR. Results evaluated on one A GPU.
xAR
BAR (without residual loss)
BAR (with residual loss)
Wall-time per iteration
1.00x
1.00
1.01x
GPU memory usage
1.00x
x.00
1.03x
E EXTENSION TO DISCRETE AR MODELS
While this paper predominantly focuses the exposition and experiments of continuous BAR mod- els, the unified framework of linear transform can also be adapted to discrete AR paradigms. The rationale for prioritizing continuous BAR models herein is that they avoid the quantization of the output introduced by VQ-VAEs. Such quantization, a prerequisite step required by discrete AR models, inherently introduces loss of information. This loss can detrimentally affect the fidelity and quality of the final generated images. Consequently, the adoption of continuous AR models circumvents this quantization-indeee induced information bottleneck, facilitating superior preservation of information directly from the latent representation of VAEs.
There exist two potential strategies to extend BAR to discrete AR models. The first involves adapt- ing the principles of linear transformations and learnable hasis to the quantization stage of VQ-VAE. For instance, VAR (Tian et al. 2024) implements a manual designed hierarchical quantization, pro- gressing from global to local image features. This is achieved by resizing the outputs of VAE to various resolutions prior to quantization, effectively dedicating the initial basis to the holistic image representation, subsequent four bases to the quadrants of image, etc. In similar vein, the learned bases, as visualized in fig. [ derived from a BAR model could potentially guide the quantization of VAE latents. However, might require multi-stage training process, the joint optimization of both VQ- VAE and AR model.
The second relies and utilizes the outputs of existing VQ-VAEs. In this case, the content of each discrete token remains unaltered, and the linear transform is thereby confined to the rearrangement or regrouping of tokens the standard basis e,. The corresponding transform matrix A takes the form of permutation matrix, which consists of only 0 and 1. This is similar to RAR (Yu et al. 2024b) and PAR (Wang et al., (2024). where the former introduces random permutations of the token sequence during training, and the latter partitions the tokens into groups and prioritizes the pivot tokens. However, this approach may introduce challenges on how to optimize the matrix A while maintaining permutation matrix.
F ABLATION ON RESIDUAL Loss
Table 10: Compare offline pre-computed hasis and online learnable basis with Cresidual BAR-
Model
FID
ISt
Pre.t
Rec.t
Baseline
1.72
280.4
0.82
0.59
Offline basis
1.69
286.4
0.82
0.60
Online learnable basis
1.63
291.3
0.83
0.62
The design of our proposed Cresidual BAR in eq. 10 naturally leads to the question that can we first apply a similar residual loss on real images from dataset, then fix the offline pre-computed basis to train AR models? We conduct ablation experiments in table I0 and find that while AR models benefit from the offline basis, our online learnable basis allows adjustments to the inherit dynamics of AR models and obtains better performances.
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Table 11: DINOV.. KID, and CLIP score comparison.
2DDINOv24
KID
CLIP scoref
DiT (Peehles & Xie 2023)
77.43
0.060
0.317
SiT (Ma et al. 2024
70.52
0,055
0.326
REPA Yu 2024d)
59.16
0,052
0.334
LightningDiI Yao & Wang 2025)
56.23
0.050
0.338
BAR
52.33
0.047
0.343
Table 12: CLIPscore and HPSv2 comparison.
CLIP scoref
HPSv21
LDM
0.330
25.56
LlamaGen
0.319
24.22
FAR BAR
0.328
25.28
0.332
25.71
G MORE RESULTS
G.1 ADDITIONAL METRICS
To provide a more comprehensive evaluation beyond the commonly utilized Fréchet Inception Dis- tance (FID) (Heusel et al. 2017) and Inception Score (IS) (Salimans et al. 2016), we also incorpo- rate more metrics in table 11 including FDDINOV2 (Stein et al. 2023) and Kernel Inception Distance (KID) (Binkowski et al. 2018). Furthermore, to quantify the alignment between generated images and input conditions, ing the CLIP similarity between images and corresponding prompts. For the class culdisconiiiionll image generation task NeageNet, as detailed in table 11 the text prompt is constructed "a photo of [CLASS]", where [CLAS5] is replaced by the specific class label. the context of text-to-image models, we also present HPSv2 (Wu al. 2023) results in table I2
report the CLIP (Radford et al. 2021) score in tables 11 and 12 comput-
G.2 LEARNED BASIS VISUALIZATION
In addition to fig. we provide more visualization results of the learned basis in fig. g We attribute the discontinuous pattern of latent space FFHQ to the insufficient training, while the basis of latent space ImageNet is optimized for more iterations.
G.3 GENERATION PROCESS VISUALIZATION
In addition to fig. we provide more visualization results of the generation process by progressively decoding the generated token sequence y fig.
G.4 GENERATED SAMPLES
We present more visualization of generated samples with our BAR-H model in figs. T0 to 17 also present more rext-to-image samples our BAR model in fig. 18
We
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FFHQ (pixel space)
FFHQ (latent space)
ImageNet (latent space)
e
OU
I
20
Figure 8: Visualization of the first 20 learned basis ag. Darker regions mark higher values.
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FFHQ
ImageNet
Figure 9: We decode the generated sequences every 25 tokens. The first row uses only one token.
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Eo 0.7%
Figure 10: Generated samples of BAR-H the class "balloon" (417).
Figure 11: Generated samples of BAR-H on the class "panda" (388).
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Generated samples of BAR-H the class "golden retriever" (207).
Figure 12:
Figure 13: Generated samples of BAR-H on the
class "lion" (291).
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Figure 14:
Generated samples of BAR-H the class "space shuttle" (812).
Figure 15: Generated samples of BAR-H on the
class "valley" (979).
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Figure 16: Generated samples of BAR-H the class "volcano" (980).
Figure 17: Generated samples of BAR-H on the
class "lake shore" (975).
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whimsical candy land entirely of Jallipops, chocolate rivers, gingerbread houses under cotton candy sky.
surreal paint of large, statueqque busts suits, partially buried in vast, sandy muted sky.
A cozy,, book filled library crackling fireplace offers a warm and inviting atmosphere a snowy winter day.
A serene mountain monastery perches precariously on cliffiide, overlooking valley shrouded in morning mist.
A tranquil Japanese garden springtime, featuring koi pond. cherry blossom trees, and traditional lantems.
An enchanting fairy tale cottage with thatehed roof is nestled haside sparkling stream sun-dappled forest.
dramatic soene shows lone lighthouse bravely standing against miing, stornyy sea with crashing
A close-up of surprised, wide-eyed tabby cat sitting behind the dining table, gazing at plates potatoes the front.
A vibrunt underwater scene features a sunken ship, colorful cornl reefs, and various tropical illuminated by sunlight.
hidden waterfall
cascades into a erystal-clear pool within lush, emerald grotto, sunlight filtering through leaves.
An impressionistic painting captures bustling Parisian street cafe rainy evening with glowing reflections.
surreal dreamscape depicts flosting islands connected by shimmering. ethereal bridges under a sky of swirling colors.
nomadic desert caravan travels across vast, sun- drenched sand dunes under sky painted with hues of orange and purple.
An old-fashiooed steam train chugs through a picturesque snowy mountain landscupe, smoke billowing from its chimney.
stands desolate alien planet, gazing swirling nehula the distant, star star-filled sky.
dramatic volcanic eruption, with molten lava flowing down mountainoide under a stermy, sky.
highly detailed photogruph captures the intricate and irideseant colors ofa butterfly's delicate wings.
surreal desert onsis appears with palm trees and shimmering under sky filled with impossibly large
An abundoneed spaceship. overgrown with alien flora, silently the crimson plains of an uncxplered, dissant planct.
moss- covered stone archway opens mystical bathed the soft glow of full moon.
corry, sun-drenched
A hypemealistic close-up shows a dew-covered dragonilly resting delicately on vibrant, freshly bloomed flower.
An weuthered wonden ship sails couragcously through tumultucus, storm tossed sea towards
A tranquil shows weoden rowboar gently drifling still lake, reflecting the vibrant foliage perfectly.
surreal underwater library has bookshelves made of coral fish swimming gracefilly among floating. open books.
kitchen with freshly baked windowsill, cat peacefully napping nearby.
Figure 18: Text-to-image samples of BAR.
29


Reviews:
[{"review_id": "r9akFaytPj", "reviewer": "Reviewer_shV6", "summary": "This paper introduces Basis Autoregressive (BAR), a framework for visual autoregressive (AR) generative modeling that rethinks how image data is factorized for sequential prediction. Rather than adhering to the fixed, human-designed raster-scan order, BAR mathematically formalizes token sequences as projections onto learned basis vectors, proposing an end-to-end approach to optimize this basis using a parameterized linear transformation matrix $\\mathbf{A}$. The framework unifies various previous AR methods as special cases of matrix $\\mathbf{A}$ and claims to transcend the limitations of hand-crafted inductive biases, showing strong empirical results (notably FID of 1.15 on ImageNet-256). The paper provides theoretical justification, thorough ablations of the learned basis, and visualizations of both the basis and progressive generation.", "questions": "Please provide responses to the issues raised in my Weaknesses section.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. Unified and General Framework: BAR provides a mathematically coherent and unifying lens for understanding and extending autoregressive visual models. By interpreting previous methods as instances of linear basis transformations, the paper brings much-needed formalism to a field heavily reliant on heuristics.\n2. Mathematical Depth and Rigor: The paper gives detailed derivations and proofs (see Section 3.3, and Appendix A) demonstrating the theoretical validity and equivalence of BAR to well-known AR objectives (e.g., MAR, xAR), subject to the choice of loss and basis.\n3. Visualization: Visualization of generation (Figures 4, 8, 9) and qualitative samples (Figures 5, 10, 11) effectively demonstrate the dynamics and diversity of the BAR approach.", "weaknesses": "1. Experimental Reproducibility Gaps: While the main algorithm and hyperparameters are explained (see Section C and Table 8), some necessary details for replication are spread across appendices and main text, and others (e.g., code availability, certain training curves beyond ImageNet, data preprocessing for alternative datasets) are left somewhat vague. For a contribution at this level, full transparency would further strengthen the impact.\n2. Dependence on VAE/Tokenizer Quality: Since the BAR method operates atop latent tokens produced via VAE or similar encoders (e.g., KL-16 tokenizer), its success is inextricably tied to the information bottleneck of the encoder. While this is noted in the limitations, reliance on a potentially lossy front-end may restrict the impact in domains where end-to-end optimization is required.\n3. Clarity and Structure Issues: The mathematical notation is dense and sometimes overly compressed. For example, the definitions of prefix sums and the role of the reverse transform $\\mathbf{A}^{-1}$ in generation/decoding steps are not always explicitly illustrated or described in algorithmic terms (see Figure 2 and the pseudo-code).\nSome implementation choices, such as hard vs. soft orthogonal projection, are only detailed in ablation (Table 6) and could use a deeper explanation in the main text.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ih186LgF53", "reviewer": "Reviewer_e8ty", "summary": "This paper proposes BAR (Basis Autoregressive), a new paradigm for AR visual generation. Instead of following a fixed raster-scan token prediction order, BAR introduces a learnable linear transform matrix A that redefines the basis of token prediction space. The authors claim that existing AR variants (e.g., VAR, RAR, PAR, FAR, xAR) can be expressed as special cases of A. They further propose a residual training objective to encourage informative early tokens and show extensive experiments achieving FID 1.15 on ImageNet-256, surpassing diffusion and AR baselines. The method is compatible with both MAR and xAR architectures and improves efficiency while reducing inductive bias.", "questions": "1. Does A converge to a stable configuration, or does it keep drifting during training? Any visualization of A evolution?\n2. Can BAR be applied to autoregressive text LLMs? If not, what limits the transfer?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Unified theoretical framework: Reformulates a broad range of AR improvements under a single matrix transformation paradigm, offering conceptual clarity.\n2. Learnable basis with end-to-end training reduces reliance on handcrafted heuristics and inductive biases.\n3. Strong empirical results: Achieves new SOTA on ImageNet-256 and competitive performance on ImageNet-512 and text-to-image tasks.\n4. Compatible with multiple AR architectures (MAR, xAR), indicating generality rather than architecture-specific tweaking.\n5. Residual objective design mimics coarse-to-fine prediction in a principled way rather than manually defining scales.\n6. Visualization of learned basis provides interpretability insights into the emergence of hierarchical token prediction.", "weaknesses": "1. **Theoretical depth vs. practical benefit**: While the “unified” perspective is appealing, the core operation (learnable linear transform on tokens) is conceptually simple. The novelty may be perceived as incremental unless the generality claim is further formalized or proven beyond examples.\n2. **Orthogonality constraint and optimization stability**: The reliance on orthogonal projection raises the question of whether the learned A collapses to simple permutations or low-rank patterns. More analysis is needed.\n3. **Lack of ablation on scalability of A**: The matrix is N×N, which scales quadratically with sequence length. It's unclear how this approach behaves at 1024+ tokens or 1024² resolution.\n4. **Training cost overhead**: The paper reports inference-time speedup but does not clearly quantify the extra training overhead introduced by optimizing A.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "8I4cToB1o3", "reviewer": "Reviewer_WUrW", "summary": "The paper proposes Basis Autoregressive (BAR), a novel paradigm that reformulates autoregressive (AR) image generation by viewing token sequences as basis vectors in a linear space. Traditional AR models generate images in raster-scan order, which disregards spatial structure and heavily depends on human-designed heuristics. BAR achieves state-of-the-art FID 1.15 on ImageNet-256, demonstrates scalability to 512×512 resolution, and generalizes to text-to-image tasks with consistent improvements across metric", "questions": "1. Does the orthogonality constraint limit the expressivity of (A)? Would relaxing it (e.g., via low-rank factorization) yield additional improvements?\n2. How does BAR perform in **long-sequence autoregression** (e.g., 1k+ tokens), where cumulative numerical error in (A^{-1}) may become significant?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "BAR reformulates AR models as linear-space transformations, offering a mathematically elegant and generalizable view that subsumes prior ad hoc approaches.\n\nThe introduction of an orthogonal, end-to-end learnable transform matrix A replaces human inductive biases with data-driven optimization.\n\nBAR achieves new SOTA on multiple benchmarks (e.g., FID 1.15 on ImageNet-256) and demonstrates speed–quality advantages with fewer parameters.", "weaknesses": "1. While mathematically rigorous, the paper could better explain the intuition behind how the learned basis improves spatial dependency modeling.\n2. The exploration of non-orthogonal or adaptive-rank transformations could broaden the framework’s generality.\n3. Although efficiency is claimed, a detailed analysis of training overhead (from learning (A)) versus vanilla AR would be valuable.\n4.  The connection between BAR’s linear transform and classical linear subspace learning (e.g., PCA, ICA) is briefly implied but not discussed explicitly.\n5.  Equation (9)–(10) and residual objective explanation could use more intuitive narrative; some notations (e.g., (ỹ_k)) are underdefined at first appearance.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ebZK7QL6dM", "reviewer": "Reviewer_wfTF", "summary": "This paper proposes Basis Autoregressive, a unified and learnable framework for autoregressive visual generation that treats tokens as projections of an image onto a learned basis via a linear transform y = Ax. By optimizing an orthogonal, end-to-end trainable transform matrix A jointly with the AR model, BAR refactors token sequences into more informative orders and units, theoretically preserving equivalence to MAR and xAR objectives and practically improving generation. A residual objective encourages early bases to capture maximal information. BAR subsumes prior designs (e.g., VAR, PAR, RAR, FAR, xAR) as special cases and achieves state-of-the-art results on ImageNet-256, with additional results of ImageNet-512, text-to-image generation, and extensive ablations.", "questions": "* Why can A be trained end-to-end jointly with the AR model? What outcomes would we expect from a two-stage training scheme instead?\n\n* In Appendix Figure 18, the quality of text-to-image results does not look good, with many high-frequency artifacts. Please explain the likely causes.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "* The proposed BAR paradigm is fresh and compelling, offering a unified framework that theoretically derives and subsumes a range of recent AR variants.\n* The method is simple and end-to-end trainable without complicated designs. \n* It achieves strong results on ImageNet-256, comparable to current state-of-the-art diffusion models, and also includes extensive ablations that validate the effectiveness of each component. The paper also validates its scalability in terms of model size, resolution, and data scale (t2i generation).\n* The paper is clearly written, well-structured, and easy to follow.", "weaknesses": "I do not see any major flaws in this paper. I have a few discussion points, and if addressed, I would be happy to raise my score:\n\n* The residual loss feels somewhat heuristic. The paper’s motivation critiques recent AR work for relying on hand-crafted inductive biases, yet the residual loss reintroduces a prefix-ordering bias. More diagnostics on how the learned ordering correlates with information content, and comparisons to alternative ordering regularizers, would clarify why this particular choice is preferable.\n\n* Orthogonality constraint on A: While enforcing orthogonality yields clean equivalence to MAR/xAR and stabilizes training, it restricts the search space to energy-preserving transforms. It remains unclear whether relaxing to general invertible A could provide further gains. An exploration of non-orthogonal parameterizations would be valuable.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)