arxiv: 2605.01220 · v1 · submitted 2026-05-02 · 💻 cs.CV

Recognition: unknown

Visual Implicit Autoregressive Modeling

Pengfei Jiang , Jixiang Luo , Luxi Lin , Zhaohong Huang , Xuelong Li

Authors on Pith no claims yet

Pith reviewed 2026-05-09 15:17 UTC · model grok-4.3

classification 💻 cs.CV

keywords visual autoregressive modelingimplicit equilibrium layersimage generationImageNet benchmarkFID scoreJacobian-free backpropagationcompute efficiencynext-scale prediction

0 comments

The pith

VIAR embeds an implicit equilibrium layer in next-scale autoregressive generation to match VAR quality with 38% of the parameters and flexible inference compute.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes Visual Implicit Autoregressive Modeling by inserting an implicit equilibrium layer into a shallow next-scale prediction network. This layer is trained using Jacobian-Free Backpropagation to keep training memory constant regardless of iteration depth. At inference, the number of fixed-point iterations per scale can be adjusted to trade compute for quality or speed. On the ImageNet 256x256 benchmark the resulting model reaches an FID of 2.16 and sFID of 8.07 while using only 38.4 percent of the parameters required by the explicit VAR baseline. The same model can halve peak memory and double throughput on a single GPU without any retraining, and it also improves zero-shot in-painting and class-conditional editing.

Core claim

VIAR is a next-scale autoregressive generator that places an implicit equilibrium layer between shallow pre- and post-processing blocks. The layer is trained end-to-end with Jacobian-Free Backpropagation, which yields constant training memory. At inference the layer can be unrolled for an arbitrary number of steps per scale, exposing a direct knob on compute budget. The approach attains FID 2.16 and sFID 8.07 on ImageNet 256x256 with 38.4% of VAR's parameters and remains competitive with large diffusion models.

What carries the argument

Implicit equilibrium layer placed between shallow pre/post blocks and trained with Jacobian-Free Backpropagation; it converges to a fixed point whose iteration count can be chosen independently at inference.

Load-bearing premise

The implicit equilibrium layer converges reliably under Jacobian-Free Backpropagation and that the per-scale iteration count can be varied post-training without degrading the learned fixed point.

What would settle it

Running the trained VIAR model with iteration counts both higher and lower than those used during training and checking whether FID and sFID remain stable or improve; a large degradation would indicate that the fixed point is not robust to post-training changes in iteration depth.

Figures

Figures reproduced from arXiv: 2605.01220 by Jixiang Luo, Luxi Lin, Pengfei Jiang, Xuelong Li, Zhaohong Huang.

**Figure 1.** Figure 1: Resource savings of VIAR versus VAR. (a) By collapsing the explicit middle stack into a single implicit layer, VIAR reduces the total parameters by 61.6% and the middle-block parameters by 93.3%. (b) Its implicit design with adaptive per-scale iteration further lowers the GPU memory size during parallel next-scale prediction by 42.0%. (c) Despite this extreme lightweight configuration, VIAR maintains stro… view at source ↗

**Figure 2.** Figure 2: Overview of VIAR. (a) The Implicit Architecture. We replace the deep explicit VAR stack with a single implicit equilibrium layer between shallow pre/post-layers. Training via Jacobian-Free Backpropagation unrolls only the last m iterations for gradients, ensuring constant memory usage. (b) VIAR Generation Process. During inference, unlike standard VAR which is constrained to fixed computation, VIAR flexib… view at source ↗

**Figure 3.** Figure 3: Convergence analysis of the implicit equilibrium layer at high-resolution scales. We measure the cosine similarity between the last two steps of the iteration at the largest scale. The similarity achieves 0.985 by iteration 5 and approaches 0.999 by iteration 10, indicating that the fixed-point iteration converges rapidly. The corresponding FID changes on the right further support this point. This rapid co… view at source ↗

**Figure 4.** Figure 4: Qualitative comparison on ImageNet 256 × 256. For each class we sample with identical decoding settings. Left: VAR; right: VIAR. VIAR matches or surpasses the visual quality of VAR while using fewer parameters and achieving faster inference. VAR (GPU Mem: 19.24 GB; Throughput: 15.16 images/s) VIAR (GPU Mem: 8.53 GB; Throughput: 32.08 images/s) view at source ↗

**Figure 6.** Figure 6: Training memory vs. explicit depth. Left: parameter/gradient memory, right: optimizer-state memory. VAR’s memory grows roughly linearly with depth, whereas VIAR stays essentially constant because the implicit equilibrium architecture. practice, s4 offers the best latency–memory profile for interactive use, while s1 and s2 provide the strongest quality under tighter but still favorable budgets. Overall,… view at source ↗

**Figure 7.** Figure 7: Zero-shot generalization of VIAR: in-painting and class-conditional editing without finetuning. For in-painting, tokens outside the mask are teacher-forced and the model generates only the masked region; for class-conditional editing, the model synthesizes content inside a bounding box given a class label while keeping the rest unchanged. Columns show original vs. generated results for VAR and VIAR. VIAR p… view at source ↗

**Figure 8.** Figure 8: FID versus parameters for explicit VAR and our VIAR. VIAR attains near SOTA quality with substantially fewer parameters. We compare the deeply explicit stacked VAR against our VIAR. The tokenizer, data, and training protocol are identical. The parameter–FID frontier in view at source ↗

**Figure 9.** Figure 9: More visual results of VIAR on ImageNet. Samples are generated with a constant iteration count of 10 across all scales. 14 view at source ↗

read the original abstract

Visual Autoregressive Modeling (VAR) based on next-scale prediction achieves strong generation quality, but their explicit deep stacks fix the amount of computation per scale and inflate memory at high resolutions. We introduce Visual Implicit Autoregressive Modeling (VIAR), a next-scale autoregressive generator that embeds an implicit equilibrium layer between shallow pre/post blocks. The implicit layer is trained with Jacobian-Free Backpropagation, yielding constant training memory, while inference exposes a per-scale iteration knob that enables compute control. On ImageNet 256x256 benchmark, VIAR attains FID 2.16, and sFID 8.07 with only 38.4% parameters of VAR, matching or surpassing strong AR baselines and remaining competitive with large diffusion models. By controlling the per-scale knob, VIAR can reduce peak memory from 19.24 GB to 8.53 GB and doubles throughput from 15.16 to 32.08 images/s on a single RTX 4090, without retraining. Ablations show that fewer steps are sufficient for fixed-point iterations to converge and that VIAR consistently dominates VAR across quality efficiency operating points. In zero shot in-painting and class-conditional editing, VIAR produces sharper details and smoother boundaries while preserving global structure, validating the benefits of implicit equilibria and per-scale compute control for practical, deployable visual generation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

VIAR swaps an implicit equilibrium layer into next-scale VAR, trained via JFB, to cut memory and let users dial compute per scale at inference while keeping competitive FID.

read the letter

The core move is embedding an implicit equilibrium layer between shallow pre- and post-blocks in a next-scale autoregressive generator, trained with Jacobian-free backpropagation. This keeps training memory constant and gives a per-scale iteration knob at inference that the abstract says can be adjusted post-training without retraining. On ImageNet 256x256 they report FID 2.16 and sFID 8.07 using 38.4% of VAR's parameters, plus clear memory drop from 19.24 GB to 8.53 GB and throughput doubling to 32 images/s on an RTX 4090. Ablations indicate fewer fixed-point steps suffice and that the model stays ahead of VAR across quality-efficiency points. Zero-shot inpainting and editing examples look sharper at boundaries while holding global structure. That combination of implicit modeling with scale-wise AR is not something I recall seeing in the cited prior work, and the practical efficiency numbers are the part that would interest deployment-focused readers. The soft spot is exactly the one the stress-test flags: the claim that the learned fixed point stays stable and quality holds when you change the iteration count after training rests on the JFB training producing a reliable attractor. The abstract mentions ablations showing convergence with fewer steps, but without training curves, residual plots, or explicit checks that quality is insensitive to the knob across a range, it is hard to judge how robust the control really is. If the fixed-point residual does not decay cleanly or shifts with budget, the deployability argument weakens. The baselines appear standard and the metrics are reported directly, but full experimental details would be needed to confirm no hidden implementation advantages. This is the kind of paper that matters for people building resource-aware image generators who already know VAR and want a drop-in way to trade compute for memory. It is coherent on its own terms and shows honest engagement with the efficiency problem, so it deserves a serious referee even if the convergence details need tightening in revision.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes Visual Implicit Autoregressive Modeling (VIAR), extending next-scale Visual Autoregressive Modeling (VAR) by inserting an implicit equilibrium layer between shallow pre- and post-processing blocks. The layer is trained via Jacobian-Free Backpropagation to keep training memory constant, while inference exposes a tunable per-scale iteration count for compute-quality trade-offs. On ImageNet 256×256 the model reports FID 2.16 and sFID 8.07 at 38.4 % of VAR’s parameter count, together with memory reduction (19.24 GB → 8.53 GB) and doubled throughput (15.16 → 32.08 img/s) on a single RTX 4090 without retraining. Ablations and zero-shot inpainting/editing results are presented to support the benefits of implicit equilibria and per-scale control.

Significance. If the implicit fixed-point convergence and post-training iteration flexibility hold, VIAR would provide a practical mechanism for dynamic compute allocation in autoregressive image generators, improving deployability while remaining competitive with both AR and diffusion baselines. The reported parameter efficiency and memory/throughput gains would constitute a meaningful advance for high-resolution visual generation.

major comments (2)

[Experiments / Ablations] The central efficiency claims (memory reduction from 19.24 GB to 8.53 GB and throughput doubling) rest on the assumption that the implicit equilibrium layer, trained with Jacobian-Free Backpropagation, reaches a stable fixed point whose quality is insensitive to the number of inference iterations chosen after training. No explicit fixed-point residual curves, convergence-rate analysis, or ablation on iteration-budget sensitivity appear in the reported experiments, leaving the weakest assumption identified in the stress-test note unaddressed.
[Experiments / Main Results] The headline ImageNet numbers (FID 2.16, sFID 8.07) are presented without the full set of training curves, exact baseline re-implementations, or statistical significance tests that would be required to substantiate the claim of matching or surpassing strong AR baselines at reduced parameter count. The moderate soundness rating in the reader’s assessment follows directly from this omission.

minor comments (2)

[Abstract] The phrase “zero shot in-painting” in the abstract should be hyphenated as “zero-shot inpainting” for standard terminology.
[Method] Notation for the implicit layer (e.g., the equilibrium operator and the per-scale iteration variable) should be introduced once in the method section and used consistently thereafter to avoid ambiguity when discussing the inference knob.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the potential practical benefits of VIAR for controllable inference. We address each major comment below and will incorporate revisions to strengthen the experimental support.

read point-by-point responses

Referee: [Experiments / Ablations] The central efficiency claims (memory reduction from 19.24 GB to 8.53 GB and throughput doubling) rest on the assumption that the implicit equilibrium layer, trained with Jacobian-Free Backpropagation, reaches a stable fixed point whose quality is insensitive to the number of inference iterations chosen after training. No explicit fixed-point residual curves, convergence-rate analysis, or ablation on iteration-budget sensitivity appear in the reported experiments, leaving the weakest assumption identified in the stress-test note unaddressed.

Authors: We agree that explicit visualization of fixed-point convergence would directly substantiate the core assumption. The current manuscript already states that 'fewer steps are sufficient for fixed-point iterations to converge' and reports quality-efficiency trade-offs, but we will add (i) per-scale residual curves ||f(x) - x|| over inference iterations, (ii) convergence-rate analysis across scales, and (iii) an ablation table showing FID/sFID as a function of iteration budget (e.g., 1, 3, 5, 10 iterations). These additions will be placed in a new subsection of the experiments and will confirm that quality stabilizes well before the default iteration count used for the headline numbers. revision: yes
Referee: [Experiments / Main Results] The headline ImageNet numbers (FID 2.16, sFID 8.07) are presented without the full set of training curves, exact baseline re-implementations, or statistical significance tests that would be required to substantiate the claim of matching or surpassing strong AR baselines at reduced parameter count. The moderate soundness rating in the reader’s assessment follows directly from this omission.

Authors: We acknowledge the value of additional transparency. In the revision we will (i) include training curves (loss and FID) for both VIAR and the VAR baseline in the appendix, (ii) provide exact hyper-parameter tables and code references for all re-implemented baselines, and (iii) report standard deviations from three independent runs for the main VIAR configuration. Full multi-seed statistical tests across every baseline remain computationally expensive; we will therefore note this limitation while still adding the requested curves and variance estimates to support the reported gains. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation relies on new architecture and empirical results

full rationale

The paper defines VIAR via an explicit new component—an implicit equilibrium layer inserted between shallow pre/post blocks, trained with Jacobian-Free Backpropagation to achieve constant memory and expose a post-training per-scale iteration knob. Performance metrics (FID 2.16, sFID 8.07, memory/throughput gains) are presented as direct empirical outcomes on ImageNet 256x256 against VAR baselines and diffusion models, with ablations confirming convergence behavior. No equation, claim, or result in the abstract or described chain reduces a reported prediction or fixed-point quality to a fitted parameter, self-citation, or ansatz imported from the authors' prior work; the central claims remain independent of their inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The method introduces one new architectural component (implicit equilibrium layer) and one training technique (Jacobian-free backprop) whose correctness is assumed rather than derived from prior literature.

free parameters (1)

per-scale iteration count
User-chosen knob at inference that controls compute; no fitted value stated in abstract.

axioms (1)

domain assumption The implicit layer reaches a stable fixed-point equilibrium under the chosen iteration budget.
Required for both training stability and inference control to function as described.

pith-pipeline@v0.9.0 · 5545 in / 1144 out tokens · 56056 ms · 2026-05-09T15:17:05.163107+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

35 extracted references · 11 canonical work pages · 3 internal anchors

[1]

Advances in neural information processing systems , volume=

Denoising diffusion probabilistic models , author=. Advances in neural information processing systems , volume=
[2]

Score-Based Generative Modeling through Stochastic Differential Equations

Score-based generative modeling through stochastic differential equations , author=. arXiv preprint arXiv:2011.13456 , year=

work page internal anchor Pith review Pith/arXiv arXiv 2011
[3]

Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

High-resolution image synthesis with latent diffusion models , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=
[4]

Proceedings of the IEEE/CVF international conference on computer vision , pages=

Scalable diffusion models with transformers , author=. Proceedings of the IEEE/CVF international conference on computer vision , pages=
[5]

Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

Taming transformers for high-resolution image synthesis , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=
[6]

Vector-quantized image modeling with improved vqgan.arXiv preprint arXiv:2110.04627, 2021

Vector-quantized image modeling with improved vqgan , author=. arXiv preprint arXiv:2110.04627 , year=

work page arXiv
[7]

Advances in neural information processing systems , volume=

Generating diverse high-fidelity images with vq-vae-2 , author=. Advances in neural information processing systems , volume=
[8]

Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

Autoregressive image generation using residual quantization , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=
[9]

Scaling Autoregressive Models for Content-Rich Text-to-Image Generation

Scaling autoregressive models for content-rich text-to-image generation , author=. arXiv preprint arXiv:2206.10789 , volume=

work page internal anchor Pith review arXiv
[10]

Advances in neural information processing systems , volume=

Conditional image generation with pixelcnn decoders , author=. Advances in neural information processing systems , volume=
[11]

Advances in neural information processing systems , volume=

Visual autoregressive modeling: Scalable image generation via next-scale prediction , author=. Advances in neural information processing systems , volume=
[12]

Advances in neural information processing systems , volume=

Deep equilibrium models , author=. Advances in neural information processing systems , volume=
[13]

Advances in neural information processing systems , volume=

Multiscale deep equilibrium models , author=. Advances in neural information processing systems , volume=
[14]

and Kolter, J

Torchdeq: A library for deep equilibrium models , author=. arXiv preprint arXiv:2310.18605 , year=

work page arXiv
[15]

Advances in Neural Information Processing Systems , volume=

On training implicit models , author=. Advances in Neural Information Processing Systems , volume=
[16]

Proceedings of the AAAI Conference on Artificial Intelligence , volume=

Jfb: Jacobian-free backpropagation for implicit networks , author=. Proceedings of the AAAI Conference on Artificial Intelligence , volume=
[17]

Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

Fixed point diffusion models , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=
[18]

Advances in Neural Information Processing Systems , volume=

Deep equilibrium approaches to diffusion models , author=. Advances in Neural Information Processing Systems , volume=
[19]

Advances in Neural Information Processing Systems , volume=

One-step diffusion distillation via deep equilibrium models , author=. Advances in Neural Information Processing Systems , volume=
[20]

Proceedings of the Computer Vision and Pattern Recognition Conference , pages=

Collaborative decoding makes visual auto-regressive modeling efficient , author=. Proceedings of the Computer Vision and Pattern Recognition Conference , pages=
[21]

arXiv preprint arXiv:2503.23367 , year=

Fastvar: Linear visual autoregressive modeling via cached token pruning , author=. arXiv preprint arXiv:2503.23367 , year=

work page arXiv
[22]

Accelerating auto-regressive text-to-image generation with training-free speculative jacobi decoding.arXiv preprint arXiv:2410.01699,

Accelerating auto-regressive text-to-image generation with training-free speculative jacobi decoding , author=. arXiv preprint arXiv:2410.01699 , year=

work page arXiv
[23]

Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

Grouped speculative decoding for autoregressive image generation , author=. Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=
[24]

Speculative Coupled Decoding for Training-Free Lossless Acceleration of Autoregressive Visual Generation

MC-SJD: Maximal Coupling Speculative Jacobi Decoding for Autoregressive Visual Generation Acceleration , author=. arXiv preprint arXiv:2510.24211 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[25]

arXiv preprint arXiv:2510.08994 , year=

Speculative Jacobi-Denoising Decoding for Accelerating Autoregressive Text-to-image Generation , author=. arXiv preprint arXiv:2510.08994 , year=

work page arXiv
[26]

arXiv preprint arXiv:2512.16483 , year=

StageVAR: Stage-Aware Acceleration for Visual Autoregressive Models , author=. arXiv preprint arXiv:2512.16483 , year=

work page arXiv
[27]

Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=

Frequency-aware autoregressive modeling for efficient high-resolution image synthesis , author=. Proceedings of the IEEE/CVF International Conference on Computer Vision , pages=
[28]

arXiv preprint arXiv:2506.08908 , year=

SkipVAR: Accelerating Visual Autoregressive Modeling via Adaptive Frequency-Aware Skipping , author=. arXiv preprint arXiv:2506.08908 , year=

work page arXiv
[29]

arXiv preprint arXiv:2505.19602 , year=

Memory-Efficient Visual Autoregressive Modeling with Scale-Aware KV Cache Compression , author=. arXiv preprint arXiv:2505.19602 , year=

work page arXiv
[30]

Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

Deep equilibrium optical flow estimation , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=
[31]

2009 IEEE conference on computer vision and pattern recognition , pages=

Imagenet: A large-scale hierarchical image database , author=. 2009 IEEE conference on computer vision and pattern recognition , pages=. 2009 , organization=

2009
[32]

Advances in neural information processing systems , volume=

Improved techniques for training gans , author=. Advances in neural information processing systems , volume=
[33]

Advances in neural information processing systems , volume=

Gans trained by a two time-scale update rule converge to a local nash equilibrium , author=. Advances in neural information processing systems , volume=
[34]

2024 , note=

Large-DiT-ImageNet , howpublished=. 2024 , note=

2024
[35]

Advances in neural information processing systems , volume=

Diffusion models beat gans on image synthesis , author=. Advances in neural information processing systems , volume=