ICLR 2026 论文列表

The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and the reciprocal class, successfully solves the Schrödinger Bridge (SB) problem. However, an efficient practical implementation requires a heuristic modification-alternating between fitting forward and backward time diffusion at each iteration. This modification is crucial for stabilizing training and achieving reliable results in applications such as unpaired domain translation. Our work reveals a close connection between the modified version of IMF and the Iterative Proportional Fitting (IPF) procedure-a foundational method for the SB problem, also known as Sinkhorn’s algorithm. Specifically, we demonstrate that the heuristic modification of the IMF effectively integrates both IMF and IPF procedures. We refer to this combined approach as the Iterative Proportional Markovian Fitting (IPMF) procedure. Through theoretical and empirical analysis, we establish the convergence of the IPMF procedure under various settings, contributing to developing a unified framework for solving SB problems. Moreover, from a practical standpoint, the IPMF procedure enables a flexible trade-off between image similarity and generation quality, offering a new mechanism for tailoring models to specific tasks.

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success arises from implicitly learning the data manifold rather than the full distribution. Our claim is based on a novel analysis of scores in the small-$\sigma$ regime that reveals a sharp separation of scales: information about the data manifold is $\Theta(\sigma^{-2})$ stronger than information about the distribution. We argue that this insight suggests a paradigm shift from the less practical goal of distributional learning to the more attainable task of geometric learning, which provably tolerates $O(\sigma^{-2})$ larger errors in score approximation. We illustrate this perspective through three consequences: i) in diffusion models, concentration on data support can be achieved with a score error of $o(\sigma^{-2})$, whereas recovering the specific data distribution requires a much stricter $o(1)$ error; ii) more surprisingly, learning the uniform distribution on the manifold—an especially structured and useful object—is also $O(\sigma^{-2})$ easier; and iii) in Bayesian inverse problems, the maximum entropy prior is $O(\sigma^{-2})$ more robust to score errors than generic priors. Finally, we validate our theoretical findings with preliminary experiments on large-scale models, including Stable Diffusion.

Polysemy has long been a major challenge in Mechanistic Interpretability (MI), with Sparse Autoencoders (SAEs) emerging as a promising solution. SAEs employ a shared encoder to map inputs to sparse codes, thereby amortizing inference costs across all instances. However, this parameter-sharing paradigm inherently conflicts with the MI community’s emphasis on instance-level optimality, including the consistency and stitchability of monosemantic features. We first reveal the trade-off relationships among various pathological phenomena, including feature absorption, feature splitting, dead latents, and dense latents under global reconstruction-sparsity constraints from the perspective of training dynamics, finding that increased sparsity typically exacerbates multiple pathological phenomena, and attribute this trade-off relationship to amortized inference. By reducing reliance on amortized inference through the introduction of semi-amortized and non-amortized approaches, we observed that various pathological indicators were significantly mitigated, thereby validating our hypothesis. As the first step in this direction, we propose Local Amortized SAE (LocA-SAE), a method that groups polysemantically close latents based on the angular variance. This method is designed to balance the computational cost of per-sample optimization with the limitations of amortized inference. Our work provides insights for understanding SAEs and advocates for a paradigm shift in future research on polysemy disentanglement. The code is available \url{https://github.com/wenjie1835/Local_Amotized_SAEs}.

Despite their impressive performance, generative image models trained on large-scale datasets frequently fail to produce images with seemingly simple concepts -- e.g., human hands or objects appearing in groups of four -- that are reasonably expected to appear in the training data. These failure modes have largely been documented anecdotally, leaving open the question of whether they reflect idiosyncratic anomalies or more structural limitations of these models. To address this, we introduce a systematic approach for identifying and characterizing "conceptual blindspots" -- concepts present in the training data but absent or misrepresented in a model's generations. Our method leverages sparse autoencoders (SAEs) to extract interpretable concept embeddings, enabling a quantitative comparison of concept prevalence between real and generated images. We train an archetypal SAE (RA-SAE) on DINOv2 features with 32,000 concepts -- the largest such SAE to date -- enabling fine-grained analysis of conceptual disparities. Applied to four popular generative models (Stable Diffusion 1.5/2.1, PixArt, and Kandinsky), our approach reveals specific suppressed blindspots (e.g., bird feeders, DVD discs, and whitespaces on documents) and exaggerated blindspots (e.g., wood background texture and palm trees). At the individual datapoint level, we further isolate memorization artifacts -- instances where models reproduce highly specific visual templates seen during training. Overall, we propose a theoretically grounded framework for systematically identifying conceptual blindspots in generative models by assessing their conceptual fidelity with respect to the underlying data-generating process.

Personalizing text-to-image diffusion models involves integrating novel visual concepts from a small set of reference images while retaining the model’s original generative capabilities. However, this process often leads to overfitting, where the model ignores the user’s prompt and merely replicates the reference images. We attribute this issue to a fundamental misalignment between the true goals of personalization, which are subject fidelity and text alignment, and the training objectives of existing methods that fail to enforce both objectives simultaneously. Specifically, prior approaches often overlook the need to explicitly preserve the pretrained model’s output distribution, resulting in distributional drift that undermines diversity and coherence. To resolve these challenges, we introduce a Lipschitz-based regularization objective that constrains parameter updates during personalization, ensuring bounded deviation from the original distribution. This promotes consistency with the pretrained model’s behavior while enabling accurate adaptation to new concepts. Furthermore, our method offers a computationally efficient alternative to commonly used, resource-intensive sampling techniques. Through extensive experiments across diverse diffusion model architectures, we demonstrate that our approach achieves superior performance in both quantitative metrics and qualitative evaluations, consistently excelling in visual fidelity and prompt adherence. We further support these findings with comprehensive analyses, including ablation studies and visualizations.

3D part amodal segmentation--decomposing a 3D shape into complete, semantically meaningful parts, even when occluded--is a challenging but crucial task for 3D content creation and understanding. Existing 3D part segmentation methods only identify visible surface patches, limiting their utility. Inspired by 2D amodal segmentation, we introduce this novel task to the 3D domain and propose a practical, two-stage approach, addressing the key challenges of inferring occluded 3D geometry, maintaining global shape consistency, and handling diverse shapes with limited training data. First, we leverage existing 3D part segmentation to obtain initial, incomplete part segments. Second, we introduce HoloPart, a novel diffusion-based model, to complete these segments into full 3D parts. HoloPart utilizes a specialized architecture with local attention to capture fine-grained part geometry and global shape context attention to ensure overall shape consistency. We introduce new benchmarks based on the ABO and PartObjaverse-Tiny datasets and demonstrate that HoloPart significantly outperforms state-of-the-art shape completion methods. By incorporating HoloPart with existing segmentation techniques, we achieve promising results on 3D part amodal segmentation, opening new avenues for applications in geometry editing, animation, and material assignment.

Flow map models such as Consistency Models (CM) and Mean Flow (MF) enable few-step generation by learning the long jump of the ODE solution of diffusion models, yet training remains unstable, sensitive to hyperparameters, and costly. Initializing from a pre-trained diffusion model helps, but still requires converting infinitesimal steps into a long-jump map, leaving instability unresolved. We introduce *mid-training*, the first concept and practical method that inserts a lightweight intermediate stage between the (diffusion) pre-training and the final flow map training (i.e., post-training) for vision generation. Concretely, *Consistency Mid-Training* (CMT) is a compact and principled stage that trains a model to map points along a solver trajectory from a pre-trained model, starting from a prior sample, directly to the solver-generated clean sample. It yields a trajectory-consistent and stable initialization. This initializer outperforms random and diffusion-based baselines and enables fast, robust convergence without heuristics. Initializing post-training with CMT weights further simplifies flow map learning. Empirically, CMT achieves state-of-the-art two-step FIDs of 1.97 (CIFAR-10), 1.32 (ImageNet $64\times64$), and 1.84 (ImageNet $512\times512$), using up to $98$\% less training data and GPU time than CMs. On ImageNet $256\times256$, it attains 1-step FID 3.34 with $\sim50$\% less training than MF from scratch (FID 3.43). On MSCOCO T2I, CMT reaches the best FID with $\sim47$\% less training. This establishes CMT as a principled, efficient, and general framework for training flow map models. Code and models are available at https://github.com/sony/cmt.

Traditional cartoon and anime production involves keyframing, inbetweening, and colorization stages, which require intensive manual effort. Despite recent advances in AI, existing methods often handle these stages separately, leading to error accumulation and artifacts. For instance, inbetweening approaches struggle with large motions, while colorization methods require dense per-frame sketches. To address this, we introduce ToonComposer, a generative model that unifies inbetweening and colorization into a single post-keyframing stage. ToonComposer employs a sparse sketch injection mechanism to provide precise control using keyframe sketches. Additionally, we propose a novel cartoon adaptation method with the spatial low-rank adapter (SLRA) to effectively tailor a modern video foundation model to the cartoon domain while keeping its temporal prior intact. Requiring as few as a single sketch and a colored reference frame, ToonComposer excels with sparse inputs, while also supporting multiple sketches at any temporal location for more precise motion control. This dual capability reduces manual workload and improves flexibility, empowering artists in real-world scenarios. To evaluate our model, we further created PKBench, a benchmark featuring human-drawn sketches that simulate real-world use cases. Our evaluation demonstrates that ToonComposer outperforms existing methods in visual quality, motion consistency, and production efficiency, offering a superior and more flexible solution for AI-assisted cartoon production.

In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with abundant noisy samples, assuming the corruption process is available as a black-box generator. We show that this task can be formulated as a one-sided entropic optimal transport problem and solved via an alternative minimization algorithm. We further provide a test criterion to determine whether the true underlying distribution is recoverable under per-sample information loss, and show that in otherwise unrecoverable cases, a small number of clean samples can render the distribution largely recoverable. Building on these insights, we introduce SFBD-OMNI, a bridge model-based framework that maps corrupted sample distributions to the ground-truth distribution. Our method generalizes Stochastic Forward-Backward Deconvolution (SFBD; Lu et al., 2025) to handle arbitrary measurement models beyond Gaussian corruption. Empirical studies validate our theory and demonstrate that SFBD-OMNI substantially improves recovery in the challenging regime of non-identifiable corruption processes.

Diffusion models have attained remarkable breakthroughs in the real-world super-resolution (SR) task, albeit at slow inference and high demand on devices. To accelerate inference, recent works like GenDR adopt step distillation to minimize the step number to one. However, the memory boundary still restricts the maximum processing size, necessitating tile-by-tile restoration of high-resolution images. Through profiling the pipeline, we pinpoint that the variational auto-encoder (VAE) is the bottleneck of latency and memory. To completely solve the problem, we leverage pixel-(un)shuffle operations to eliminate the VAE, reversing the latent-based GenDR to pixel-space GenDR-Pix. However, upscale with $\times$8 pixelshuffle may induce artifacts of repeated patterns. To alleviate the distortion, we propose a multi-stage adversarial distillation to progressively remove the encoder and decoder. Specifically, we utilize generative features from the previous stage models to guide adversarial discrimination. Moreover, we propose random padding to augment generative features and avoid discriminator collapse. We also introduce a masked Fourier space loss to penalize the outliers of amplitude. To improve inference performance, we empirically integrate a padding-based self-ensemble with classifier-free guidance to improve inference scaling. Experimental results show that GenDR-Pix performs 2.8$\times$ acceleration and 60% memory-saving compared to GenDR with negligible visual degradation, surpassing other one-step diffusion SR. Against all odds, GenDR-Pix can restore 4K image in only 1 second and 6 GB.

To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite their shared goal, these models have disparate algorithms, theoretical structures, and tradeoffs: discrete diffusion has the most natural domain, Gaussian diffusion has more mature algorithms, and diffusion on the simplex in principle combines the strengths of the other two but in practice suffers from a numerically unstable stochastic processes. Ideally we could see each of these models as instances of the same underlying framework, and enable practitioners to switch between models for downstream applications. However previous theories have only considered connections in special cases. Here we build a theory unifying all three methods of discrete diffusion as different parameterizations of the same underlying process: the Wright-Fisher population genetics model. In particular, we find simplicial and Gaussian diffusion as two large-population limits. Our theory formally connects the likelihoods and hyperparameters of these models and leverages decades of mathematical genetics literature to unlock stable simplicial diffusion. Finally, we relieve the practitioner of balancing model trade-offs by demonstrating it is possible to train a single model that can perform diffusion in any of these three domains at test time. Our experiments show that Wright-Fisher simplicial diffusion is more stable and outperforms previous simplicial diffusion models on conditional DNA generation. We also show that we can train models on multiple domains at once that are competitive with models trained on any individual domain.

Despite their fundamental role, it remains unclear what properties could make tokenizers more effective for generative modeling. We observe that modern generative models share a conceptually similar training objective---reconstructing clean signals from corrupted inputs, such as signals degraded by Gaussian noise or masking---a process we term \emph{denoising}. Motivated by this insight, we propose aligning tokenizer embeddings directly with the downstream denoising objective, encouraging latent embeddings that remain reconstructable even under significant corruption. To achieve this, we introduce the Latent Denoising Tokenizer (\method), a simple yet highly effective tokenizer trained to reconstruct clean images from latent embeddings corrupted via interpolative noise or random masking. Extensive experiments on class-conditioned (ImageNet $256\times256$ and $512\times512$) and text-conditioned (MSCOCO) image generation benchmarks demonstrate that our \method consistently improves generation quality across \textit{six} representative generative models compared to prior tokenizers. Our findings highlight denoising as a fundamental design principle for tokenizer development, and we hope it could motivate new perspectives for future tokenizer design. Code is available at: https://github.com/Jiawei-Yang/DeTok

Recent empirical studies have explored the idea of continuing to train a model at test-time for a given task, known as test-time training (TTT), and have found it to yield significant performance improvements. However, there is limited understanding of why and when TTT is effective. Earlier explanations mostly focused on the observation that TTT may help when applied to out-of-distribution adaptation or used with privileged data. However, the growing scale of foundation models with most test data being in-distribution questions these explanations. We instead posit that foundation models remain globally underparameterized, with TTT providing a mechanism for *specialization after generalization*—focusing capacity on concepts relevant to the test task. Specifically, under the linear representation hypothesis, we propose a model in which TTT achieves a substantially smaller *in-distribution* test error than global training. We empirically validate our model's key assumptions by training a sparse autoencoder on ImageNet, showing that semantically related data points are explained by only a few shared concepts. Finally, we perform scaling studies across image and language tasks that confirm the practical implications of our model, identifying the regimes where specialization is most effective. Beyond TTT, our results provide additional strong evidence in support of the linear representation hypothesis.

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric generative models remain computationally expensive at inference---requiring many steps of complex numerical simulation---as they are derived from dynamical measure transport frameworks such as diffusion and flow-matching on Riemannian manifolds. In this paper, we propose Generalised Flow Maps (GFM), a new class of few-step generative models that generalises the Flow Map framework in Euclidean spaces to arbitrary Riemannian manifolds. We instantiate GFMs with three self-distillation-based training methods: Generalised Lagrangian Flow Maps, Generalised Eulerian Flow Maps, and Generalised Progressive Flow Maps. We theoretically show that GFMs, under specific design decisions, unify and elevate existing Euclidean few-step generative models, such as consistency models, shortcut models, and meanflows, to the Riemannian setting. We benchmark GFMs against other geometric generative models on a suite of geometric datasets, including geospatial data, RNA torsion angles, and hyperbolic manifolds, and achieve state-of-the-art sample quality for single- and few-step evaluations, and superior or competitive log-likelihoods using the implicit probability flow.

While the performance of machine learning systems has experienced significant improvement in recent years, relatively little attention has been paid to the fundamental question: to what extent can we improve our models? This paper provides a means of answering this question in the setting of binary classification, which is practical and theoretically supported. We extend a previous work that utilizes soft labels for estimating the Bayes error, the optimal error rate, in two important ways. First, we theoretically investigate the properties of the bias of the hard-label-based estimator discussed in the original work. We reveal that the decay rate of the bias is adaptive to how well the two class-conditional distributions are separated, and it can decay significantly faster than the previous result suggested as the number of hard labels per instance grows. Second, we tackle a more challenging problem setting: estimation with _corrupted_ soft labels. One might be tempted to use calibrated soft labels instead of clean ones. However, we reveal that _calibration guarantee is not enough_, that is, even perfectly calibrated soft labels can result in a substantially inaccurate estimate. Then, we show that isotonic calibration can provide a statistically consistent estimator under an assumption weaker than that of the previous work. Our method is _instance-free_, i.e., we do not assume access to any input instances. This feature allows it to be adopted in practical scenarios where the instances are not available due to privacy issues. Experiments with synthetic and real-world datasets show the validity of our methods and theory.

Solving math problems through verifiable languages such as Lean has significantly impacted both the mathematics and computer science communities. Current state-of-the-art models are often trained with expensive online Reinforcement Learning (RL) or expert iteration. However, these approaches rely on fixed problem sets, which causes inefficient training and limits the model to tackle complex problems. To overcome these limitations, we propose **GAR**: *Generative Adversarial Reinforcement learning*, a comprehensive RL training framework that jointly trains the problem composer and solver in an adversarial loop. **GAR** introduces an implicit curriculum learning mechanism, which aligns task difficulty with the prover's evolving capability. It thereby improves the training efficiency and enables stronger performance of proving advanced theorems. Experiments show that with **GAR** training, Goedel-Prover-V2-8B and DeepSeek-Prover-V2-7B achieve an average relative improvement in pass@32 of **4.20%** on MiniF2F-Test benchmark, while DeepSeek-Prover-V2's pass@32 on ProofNet-Test increases from 22.58% to **25.81%**. Beyond formal proving, **GAR** establishes a general RL paradigm for co-evolution of problem generation and solving under verifiable environments.

Diffusion models deliver state-of-the-art image quality. However, sampling is costly at inference time because it requires many model evaluations (number of function evaluations, NFEs). To reduce NFEs, classical ODE multistep methods have been adopted. Yet differences in the choice of prediction type (noise/data/velocity) and integration domain (half log-SNR/noise-to-signal ratio) lead to different outcomes. We introduce Dual-Solver, which generalizes multistep samplers by introducing learnable parameters that continuously (i) interpolate among prediction types, (ii) select the integration domain, and (iii) adjust the residual terms. It maintains the traditional predictor-corrector structure and guarantees second-order local accuracy. These parameters are learned with a classification-based objective using a frozen pretrained classifier (e.g., ViT or CLIP). On ImageNet class-conditional generation (DiT, GM-DiT) and text-to-image (SANA, PixArt-$\alpha$), Dual-Solver improves FID and CLIP scores in the low-NFE regime ($3\le$ NFE $\le 9$) across backbones.

Latent generative modeling has become the standard strategy for Diffusion Transformers (DiTs), but the autoencoder has barely evolved. Most DiTs still use the legacy VAE encoder, which introduces several limitations: large convolutional backbones that compromise architectural simplicity, low-dimensional latent spaces that restrict information capacity, and weak representations resulting from purely reconstruction-based training. In this work, we investigate replacing the VAE encoder–decoder with pretrained representation encoders (e.g., DINO, SigLIP, MAE) combined with trained decoders, forming what we call \emph{Representation Autoencoders} (RAEs). These models provide both high-quality reconstructions and semantically rich latent spaces, while allowing for a scalable transformer-based architecture. A key challenge arises in enabling diffusion transformers to operate effectively within these high-dimensional representations. We analyze the sources of this difficulty, propose theoretically motivated solutions, and validate them empirically. Our approach achieves faster convergence without auxiliary representation alignment losses. Using a DiT variant with a lightweight wide DDT-head, we demonstrate state-of-the-art image generation performance, reaching FIDs of 1.18 @256 resolution and 1.13 @512 on ImageNet.

Protein folding models have achieved groundbreaking results typically via a combination of integrating domain knowledge into the architectural blocks and training pipelines. Nonetheless, given the success of generative models across different but related problems, it is natural to question whether these architectural designs are a necessary condition to build performant models. In this paper, we introduce SimpleFold, the first flow-matching based protein folding model that solely uses general purpose transformer blocks}. Protein folding models typically employ computationally expensive modules involving triangular updates, explicit pair representations or multiple training objectives curated for this specific domain. Instead, SimpleFold employs standard transformer blocks with adaptive layers and is trained via a generative flow-matching objective with an additional structural term. We scale SimpleFold to 3B parameters and train it on approximately 9M distilled protein structures together with experimental PDB data. On standard folding benchmarks, SimpleFold-3B achieves competitive performance compared to state-of-the-art baselines, in addition SimpleFold demonstrates strong performance in ensemble prediction which is typically difficult for models trained via deterministic reconstruction objectives. SimpleFold challenges the reliance on complex domain-specific architectures designs in protein folding, opening up an alternative design space for future progress.