ICML 2026 Papers

International Conference on Machine Learning

Decision breakdown

6,341papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Spotlight
    5368.5%
  • Poster
    5,80591.5%

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Towards Trustworthy and Identifiable Virtual Face Generation

Chunyang Li, Haoyue Wang, Zhenxing Qian, Sheng Li, Xinpeng Zhang, Jian Liu, Yixuan Pei, Weiqiang Wang

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Identifiable virtual face (IVF) generation aims to transform a user's original face into a virtual face for high utility privacy protection. The IVF is visually and statistically different from the original face, which can still be used for recognizing the user's identity. Despite this advantage, these schemes are unable to verify the trustworthiness of the IVF, the quality and controllability of which is often limited. To address these issues, we propose TIVDiff, a diffusion-based framework for trustworthy and identifiable virtual face generation. TIVDiff learns a virtual identity (VID) space via Virtual Identity Projection (VIP) and synthesizes high-quality virtual faces conditioned on VID and 3D facial geometry for pose and expression preservation. To enable the trustworthiness of IVF, we further propose an Identity-Guarded Generative Watermarking (IGGW) scheme to bind the diffusion initial noise with VID through a reversible mapping mechanism. This enables the embedding of an imperceptible cue into IVF for legitimacy verification. Experiments demonstrate the advantage of our TIVDiff over the state-of-the-art IVF generation schemes in terms of image quality, identifiability and trustworthiness.

Poster
Concept-Guided Tokenization: Closing the Gap Between Reconstruction and Generation

Yunqiao Yang, Haokun Lin, Guanzhong Wu, Ying Wei

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Recent advances in image generation have been largely driven by image tokenization, which compresses raw pixels into compact latent representations. While existing tokenizers excel at preserving low-level visual details through reconstruction-based training, they often lack explicit semantic guidance, which limits their ability to capture semantically structured representations and thus hinders their performance on downstream tasks like image generation. To overcome this limitation, we propose a novel tokenization framework that incorporates high-level semantics through two key innovations: (1) a text-integrated encoder that jointly processes images and textual descriptions to produce semantically enriched latent representations, and (2) a concept-guided training objective that leverages sparse autoencoders to decompose pre-trained vision-language model features to a semantic concept space, employing sparse and disentangled concept indices for guidance. Our approach achieves strong alignment with semantic concepts, maintaining high reconstruction fidelity with an rFID of 1.39 on ImageNet, while achieving a gFID of 2.65 on the class-conditional image generation task and 10.73 on the text-to-image generation task. By infusing high-level semantic structures into low-level visual fidelity, our method bridges the reconstruction-generation divide and drives generative modeling as a powerful foundation. The code is available at https://github.com/hustyyq/ConceptTok

Poster
Generation Enhances Understanding in Unified Multimodal Models via Multi-Representation Generation

Zihan Su, Hongyang Wei, Kangrui Cen, Yong Wang, Guanhua Chen, Chun Yuan, Xiangxiang Chu

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Unified Multimodal Models (UMMs) integrate both visual understanding and generation within a single framework. Their ultimate aspiration is to create a cycle where understanding and generation mutually reinforce each other. While recent post-training methods have successfully leveraged understanding to enhance generation, the reverse direction of utilizing generation to improve understanding remains largely unexplored. In this work, we propose UniMRG (Unified Multi-Representation Generation), a simple yet effective architecture-agnostic post-training method. UniMRG enhances the understanding capabilities of UMMs by incorporating auxiliary generation tasks. Specifically, we train UMMs to generate multiple intrinsic representations of input images, namely pixel (reconstruction), depth (geometry), and segmentation (structure), alongside standard visual understanding objectives. By synthesizing these diverse representations, UMMs capture rich complementary information regarding appearance, spatial relations, and structural layout. Consequently, UMMs develop a deeper and more comprehensive understanding of visual inputs. Extensive experiments across diverse UMM architectures demonstrate that our method notably enhances fine-grained perception, reduces hallucinations, and improves spatial understanding, while simultaneously boosting generation capabilities.

Poster
LineageFlow: Flow Matching for High-Fidelity Family-Aware Protein Sequence Generation

Langzhang Liang, Ming Yang, Feng Yi, Junfan Li, Shirui Pan, Xu Yinghui, Tianlei Ying, YIZHEN ZHENG, Zenglin Xu

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Protein sequence generation for engineering requires samples that are biophysically plausible and, when targeting a family/domain, remain recognizable members while exploring within-family diversity. Current discrete generative models typically start from uniform or masked-token noise, which discards strong position-specific constraints induced by evolution and forces the model to reconstruct conserved residues from scratch, leading to weak family control and low foldability. We propose \emph{LineageFlow}, a simplex-valued flow-matching model that initializes generation from lineage priors derived from ancestral sequence reconstruction, turning generation into structured mutation from an evolved scaffold. Across diverse protein families, LineageFlow achieves family validity close to held-out natural sequences and improves predicted structural confidence over uniform-/mask-initialized baselines while maintaining substantial within-family novelty and diversity, even surpassing a large pretrained baseline trained on substantially more data. Finally, we introduce \emph{rerouting}, a single intermediate-time mutate--select--amplify intervention that enables objective-guided sampling without per-step predictor guidance and yields further gains in plausibility, including a zero-shot enzyme generation case study.

Poster
Variational Learning for Insertion-based Generation

Yangtian Zhang, Zhe Wang, Arthur Gretton, Rex Ying, David van Dijk, Michalis Titsias, Jiaxin Shi

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Non-monotonic sequence generation methods, such as masked diffusion models, provide a flexible alternative to left-to-right autoregressive modeling by allowing tokens to be generated in non-fixed and prescribed orders. Despite their practical advantages, most existing non-monotonic models are order-agnostic and rely on a fixed-length grid, limiting their ability to support variable-length generation and adaptive insertion order. In this work, we introduce a probabilistic framework for learning insertion order in variable-length insertion models. We formalize a bijective correspondence between insertion trajectories and permutations, which enables an exact reparameterization of the data likelihood as a sum over permutations. Building on this result, we propose the Insertion Process (IP), a stochastic generative model that jointly learns where to insert, what to insert, and when to terminate, trained via permutation-based variational inference. Unlike prior fixed-canvas approaches, IP natively supports variable-length generation and learns data-driven preferences over insertion orders. Experiments on goal-conditioned planning and molecular string generation demonstrate that learning insertion order improves both modeling quality and generalization in domains without a canonical left-to-right structure.

Spotlight
SAMT: Generating Structured Avatar Meshes and Textures from a Single Image

Muyu Wang, Jianzhe Gao, Xingping Dong, Yujia Wang, Wenguan Wang

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Despite rapid progress in generative 3D creation, producing high-fidelity 3D face assets from a single image remains challenging, as it requires both identity-critical facial micro-structures and fine-grained view-consistent textures. To address this, we present a two-stage framework named **SAMT** for monocular 3D avatar generation and texture synthesis. Specifically, a latent 3D diffusion model for facial mesh generation is pretrained and then further adapted to generate high-quality facial geometry through large-scale domain-specific finetuning on 35K curated 3D avatar models. Subsequently, the generated facial mesh is textured through a multi-view-aware texturing strategy. It incorporates multi-view facial priors along with the mesh geometry to guide a 2D texturing diffusion, enabling cross-view consistent and mesh-aligned texture synthesis. Extensive experiments demonstrate that SAMT improves over existing baselines by producing more coherent facial geometry together with more fine-grained and view-consistent textures. Project page is available at https://github.com/muyuWang/SAMT.

Poster
Spectral Evolution Search: Efficient Inference-Time Scaling for Reward-Aligned Image Generation

Jinyan Ye, Zhongjie Duan, Zhiwen Li, Cen Chen, Daoyuan Chen, Yaliang Li, Yingda Chen

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Inference-time scaling offers a flexible way to align visual generative models with downstream objectives without updating model parameters. In modern image generation models, a natural way to do this is to optimize the random noise from which generation starts. However, searching in this high-dimensional noise space is highly inefficient, because many directions have little effect on the final image. We trace this inefficiency to a spectral bias in generative dynamics: model sensitivity to initial perturbations decays rapidly as frequency increases. Based on this insight, we propose Spectral Evolution Search (SES), a plug-and-play framework for initial noise optimization that performs gradient-free evolutionary search in a low-frequency subspace. Theoretically, we derive the Spectral Scaling Prediction from perturbation propagation dynamics, which explains the frequency-dependent impact of perturbations. Extensive experiments across diverse settings show that SES substantially improves the trade-off between generation quality and computational cost, consistently outperforming strong baselines under the same compute budget.

Poster
LithoGRPO: Fast Inverse Lithography via GRPO Reinforced Flow Matching

Yao Lai, Xuyuan Xiong, Zeyue Xue, Guojin Chen, Jing Wang, Xihui Liu, Rui Zhang, Robert D. Mullins, Bei Yu, Ping Luo

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In semiconductor manufacturing, lithography projects circuit layouts onto silicon wafers through an optical mask. As circuit features shrink below the wavelength of light, optical diffraction causes the printed patterns to deviate from their intended layouts. Inverse Lithography Technology (ILT) addresses this challenge by generating optimized masks that enhance the fidelity of pattern transfer onto wafers. While ILT resembles an image synthesis task, its reliance on explicit physical metrics for mask evaluation limits the applicability of existing generative models. We introduce LithoGRPO, an ILT framework that integrates the flow‑matching paradigm with GRPO‑based reinforcement learning (RL) fine‑tuning, enabling efficient exploration of diverse masks for a given target layout. Unlike purely generative or optimization‑based approaches, RL in LithoGRPO exploits the explicitly defined, physics‑based reward function of ILT, enabling optimization under complex, process‑aware constraints. To the best of our knowledge, this is the first framework that unifies flow matching and RL for mask optimization. To improve RL sampling efficiency, we propose a fast shot-counting algorithm for manufacturability evaluation, achieving over 130× speedup while preserving the mask ranking of the traditional shot-count metric. Extensive experiments demonstrate that LithoGRPO achieves state‑of‑the‑art performance over both optimization‑based and learning‑based methods, while maintaining efficient mask generation.

Poster
Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generation

Lei Tong, Zhihua Liu, Chaochao Lu, Dino Oglic, Tom Diethe, Philip Alexander Teare, Sotirios A. Tsaftaris, Chen Jin

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We present Causal-Adapter, a modular framework that adapts frozen text-to-image diffusion backbones for counterfactual image generation. Our method enables causal interventions on target attributes while preserving all other aspects of the image, including the core identity. In contrast to prior approaches that rely on prompt engineering without explicit causal structure, Causal-Adapter leverages structural causal modeling augmented with two attribute regularization strategies: prompt-aligned injection, which aligns causal attributes with textual embeddings for precise semantic control, and a conditioned token contrastive loss to disentangle attribute factors and reduce spurious correlations. Causal-Adapter achieves state-of-the-art results on synthetic and real-world datasets, outperforming other baselines in effectiveness, composition, realism, and minimality. These results demonstrate that the approach enables efficient, robust, and generalizable counterfactual image editing with faithful attribute modification and strong preservation of core identity.

Poster
Efficient Learned Image Compression without Entropy Coding

Hao Cao, Wenqi Guo, Zhijin Qin, Jungong Han

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Entropy coding is widely used in typical learned image compression (LIC) that converts latents into a compact bitstream. However, entropy coding is typically sequential and becomes the coding latency bottleneck. To overcome it, we present **E**ntropy-Coding **F**ree **L**earned **I**mage **C**ompression (EF-LIC), a multi-rate framework that generates compact representation by removing statistical and correlation redundancy with low coding latency. First, we introduce unconstrained vector quantization and prove that its index distribution approaches the maximum-entropy bound, yielding minimal statistical redundancy. Second, we propose a context-conditioned autoregressive transform that directly reparameterizes the latents to reduce inter-dependency. Theoretical analysis shows that EF-LIC can remove correlation redundancy as effectively as typical LIC with entropy coding, leading to comparable compression performance. Experiments show EF-LIC achieves up to 67.86\% bitrate reduction over MS-ILLM on Kodak with LPIPS. Ablation studies further show EF-LIC matches the compression performance of its entropy-coding based variant while achieving over $3\times$ faster encoding and $5\times$ faster decoding.

Poster
Language Generation with Replay: A Learning-Theoretic View of Model Collapse

Giorgio Racca, Michal Valko, Amartya Sanyal

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As scaling laws push the training of frontier large language models (LLMs) toward ever-growing data requirements, training pipelines are approaching a regime where much of the publicly available online text may be consumed. At the same time, widespread LLM usage increases the volume of machine-generated content on the web; together, these trends raise the likelihood of generated text re-entering future training corpora, increasing the associated risk of performance degradation often called *model collapse*. In practice, model developers address this concern through data cleaning, watermarking, synthetic-data policies, or, in some cases, blissful ignorance. However, the problem of model collapse in generative models has not been examined from a learning-theoretic perspective: we study it through the theoretical lens of the *language generation in the limit* framework, introducing a *replay* adversary that augments the example stream with the generator's own past outputs. Our main contribution is a fine-grained learning-theoretic characterization of when replay fundamentally limits generation: while replay is benign for the strongest notion of uniform generation, it provably creates separations for the weaker notions of non-uniform generation and generation in the limit. Interestingly, our positive results mirror heuristics widely used in practice, such as data cleaning, watermarking, and output filtering, while our separations show when these ideas can fail.

Poster
Concept Removal for Frontier Image Generative Models

Aditya Kumar, Pierre Joly, Adam Dziedzic, Franziska Boenisch

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Image generative models are trained on massive, largely uncurated internet-scale datasets that contain undesirable visual concepts. Efficiently removing such concepts from the model generations without degrading the quality of output images remains challenging. We introduce a novel concept removal method for frontier diffusion and image autoregressive models, such as, SD3.5, Flux, and Infinity. Our intervention replaces the internal bottleneck layer present in all these modern models with a transcoder that is trained to replicate the original layer while structuring it into distinct activation features. This in‑place substitution creates an integrated filter through which concept‑specific signals can be selectively disabled while preserving the rest of the model’s behavior. Since the intervention modifies the model backbone rather than attaching an external component, it remains persistent under white‑box access. Empirically, the approach achieves state‑of‑the‑art concept removal performance across modern diffusion and autoregressive models, maintains visual generation quality, provides robustness against adversarial prompts, and supports sequential removal of diverse concepts. This positions our method as a practical approach for concept removal in frontier image generative models.

Poster
Krause Synchronization Transformers

Jingkun Liu, Yisong Yue, Max Welling, Yue Song

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Self-attention in Transformers relies on globally normalized softmax weights, causing all tokens to compete for influence at every layer. When composed across depth, this interaction pattern induces strong synchronization dynamics that favor convergence toward a dominant mode, a behavior associated with representation collapse and attention sink phenomena. We introduce $\textbf{Krause Attention}$, a principled attention mechanism inspired by bounded-confidence consensus dynamics. Krause Attention replaces similarity-based global aggregation with distance-based, localized, and selectively sparse interactions, promoting structured local synchronization instead of global mixing. We relate this behavior to recent theory modeling Transformer dynamics as interacting particle systems, and show how bounded-confidence interactions naturally moderate attention concentration and alleviate attention sinks. Restricting interactions to local neighborhoods also reduces runtime complexity from quadratic to linear in sequence length. Empirically, we validate Krause Attention across diverse settings, including vision (ViT on CIFAR/ImageNet), autoregressive image generation (MNIST/CIFAR-10), large language models (Llama/Qwen), and language models trained from scratch at multiple scales (100M/200M). Across these domains, Krause Attention achieves consistent performance gains while improving computational efficiency, highlighting bounded-confidence dynamics as a scalable and effective inductive bias for attention. Project page is available at https://jingkun-liu.github.io/krause-sync-transformers/.

Poster
Rethinking 3D Shape Generation: Diffusion over Superquadrics

Zhiyang Liu, Li Wanze, Yuwei Wu, Chengran Yuan, Jiawei Sun, Rui Zheng, Marcelo H Ang Jr

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Diffusion models have advanced 3D shape generation, yet most methods still denoise in high-cardinality spaces (e.g., voxel/SDF grids, meshes, or point clouds), which is computationally and memory intensive and makes it difficult to scale in terms of both higher resolution and stronger controllability. We rethink the diffusion representation and propose to move diffusion from dense geometry to compact geometric primitives, representing each shape as a small set of **superquadrics**. Instead of operating on thousands to millions of geometric representation values, we leverage 7KB superquadric parameters (pose, size, and shape), drastically reducing diffusion-state dimensionality and per-step compute/memory. Our diffusion-over-superquadrics improves scalability by supporting broader capabilities (e.g., resolution-free point-cloud decoding, part-level editing, and constraint-based design) and achieving competitive surface-fidelity and distributional performance on standard benchmarks after point-cloud decoding, while enabling efficient generation within 0.6s per shape for most conditions.

Poster
Hyper-ICL: Attention Calibration with Hyperbolic Anchor Distillation for Multimodal In-Context Learning

Niloufar Alipour Talemi, Hossein Kashiani, Fatemeh Afghah

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Multimodal In-Context Learning (ICL) has emerged as a practical inference paradigm for Multimodal Large Language Models, where a small set of interleaved image-text In-Context Demonstrations (ICDs) conditions the model to solve new tasks. Despite its flexibility, multimodal ICL incurs high inference latency and suffers from instability due to sensitivity to demonstration formatting, ordering, and content. To address these limitations, we propose Hyper-ICL, a lightweight, training-based framework for demonstration-free multimodal ICL that reconstructs demonstration effects directly without requiring ICDs at inference time. Hyper-ICL learns a parameter-efficient low-rank logit-level adapter that calibrates attention distributions to better match demonstration-induced attention redistribution. To capture how demonstration influence varies across queries, we introduce a query-adaptive modulation mechanism that adaptively controls intervention strength at token level across layers and heads based on the current query. Finally, we propose a layer-wise hyperbolic anchor distillation loss that aligns intermediate student features to a demonstration-conditioned teacher via Lorentz geodesic distance. This loss encourages the student to reconstruct the demonstration–query relationships induced by ICDs. Extensive experiments across six different multimodal benchmarks (including VQAv2, OK-VQA, and COCO Caption) demonstrate that Hyper-ICL consistently improves accuracy and stability over vanilla ICL and existing state-of-the-art methods.

Poster
SEPS: Semantic-Enhanced Patch Slimming Framework for Fine-Grained Cross-Modal Alignment

Xinyu Mao, Junsi Li, Haoji Zhang, Yu Liang, Ming Sun

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Fine-grained cross-modal alignment is pivotal for multimodal reasoning yet remains limited by Semantic Sparsity Bias—a fundamental asymmetry where dense visual signals are under-represented by sparse textual captions. This disparity leads to the inadvertent suppression of contextually vital visual regions (patch redundancy) and hinders precise concept grounding (patch ambiguity). While Multimodal Large Language Models (MLLMs) offer rich descriptive capabilities, their naive integration often induces semantic drift due to inconsistencies with sparse ground-truth captions. To systematically resolve these challenges, we present the Semantic-Enhanced Patch Slimming (SEPS) framework. Central to SEPS is a novel Dual-Granularity Semantic Calibration mechanism, which synthesizes a Holistic Visual-Linguistic Anchor from MLLMs to synergize with original sparse queries. This mechanism transforms patch selection into a semantic consensus process, ensuring that retained patches satisfy both local discriminability and global contextual integrity. Furthermore, we propose a Salience-Guided Metric Aggregation strategy to mitigate the similarity dilution effect inherent in global mean pooling, thereby amplifying highly-relevant patch-word correspondences. Extensive experiments on Flickr30K and MS-COCO datasets demonstrate that SEPS surpasses existing state-of-the-art approaches across diverse backbones, delivering significant performance gains in text-to-image retrieval tasks. The complete implementation is available at https://anonymous.4open.science/r/SEPS/.

Poster
GADA: Geometry-Aware Deformable Aggregation for Image-Based Gaussian Splatting

Siwoo Lim, Sunjae Yoon, Gwanhyeong Koo, Chang D. Yoo

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Gaussian Splatting has achieved significant improvements by incorporating warping-based techniques. However, such methods suffer from pixel-level inaccuracies due to uncertain geometry. This uncertainty leads to spatial misalignments in the warped images, which disrupt residual learning used in warping-based methods and fundamentally limit the gains of correction, particularly on thin structures and high-frequency details. Driven by our insight that useful visual cues are not lost but locally preserved under slight displacement, we propose Geometry-Aware Deformable Aggregation (GADA). This method introduces an iterative refinement module with deformable offsets to actively correct spatial misalignments and recover these displaced cues. Furthermore, to address the limitations of standard pipelines where visibility checks (i.e., thresholding) often discard valid pixels and multi-view warped image fusion relies on naive mean aggregation, our module is coupled with an implicit confidence weighting mechanism that selectively suppresses unreliable evidence. Consequently, our approach outperforms prior warping-based Gaussian Splatting, preserving high-frequency quality while achieving 2.13 times faster FPS.

Poster
TestExplora: Benchmarking LLMs for Proactive Bug Discovery via Repository-Level Test Generation

Steven Liu, Jane Luo, Xin Zhang, Aofan Liu, Hao Liu, Jie Wu, Ziyang Huang, Yangyu Huang, Yu Kang, Scarlett Li

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Given that Large Language Models (LLMs) are increasingly applied to automate software development, comprehensive software assurance spans three distinct goals: regression prevention, reactive reproduction, and proactive discovery. Current evaluations systematically overlook the third goal. Specifically, they either constrain models to a compliance trap by treating existing code as the ground truth for regression prevention, or rely on post-failure artifacts (e.g., issue reports) for reactive bug reproduction, failing to expose defects before they manifest as failures. To bridge this gap, we present TestExplora, a benchmark designed to evaluate LLMs as proactive testers within full-scale, realistic repository environments. Comprising 2,389 tasks across 482 repositories, TestExplora conceals all defect-related information, forcing models to uncover bugs by identifying discrepancies between implementation and documentation-derived intent—utilizing documentation as the reference oracle. Furthermore, to ensure sustainable evaluation and mitigate risks of data leakage in static datasets, we propose a continuous, time-aware data collection framework. Our evaluation reveals a significant capability gap: state-of-the-art models achieve a maximum Fail-to-Pass ($F2P$) rate of only 16.06%. Further analysis indicates that navigating complex cross-module interactions and leveraging agentic exploration are critical to advancing LLMs toward autonomous software quality assurance. Consistent with this, SWEAgent instantiated with GPT-5-mini achieves an $F2P$ of 17.27% and an $F2P@5$ of 29.7%, highlighting the effectiveness and promise of agentic exploration in proactive bug discovery tasks.

Poster
Show, Don't Tell: Morphing Latent Reasoning into Image Generation

Harold Haodong Chen, Xinxiang Yin, Wen-Jie Shu, Hongfei Zhang, Zixin Zhang, Chenfei Liao, Litao Guo, Qifeng Chen, Ying-Cong Chen

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Text-to-image (T2I) generation has achieved remarkable progress, yet existing methods often lack the ability to dynamically reason and refine during generation--a hallmark of human creativity. Current reasoning-augmented paradigms mostly rely on explicit thought processes, where intermediate reasoning is decoded into discrete text at fixed steps with frequent image decoding and re-encoding, leading to inefficiencies, information loss, and cognitive mismatches. To bridge this gap, we introduce **LatentMorph**, a novel framework that seamlessly integrates implicit latent reasoning into the T2I generation process. At its core, LatentMorph introduces four lightweight components: (***i***) a **condenser** for summarizing intermediate generation states into compact visual memory, (***ii***) a **translator** for converting latent thoughts into actionable guidance, (***iii***) a **shaper** for dynamically steering next image token predictions, and (***iv***) an RL-trained **invoker** for adaptively determining when to invoke reasoning. By performing reasoning entirely in continuous latent spaces, LatentMorph avoids the bottlenecks of explicit reasoning and enables more adaptive self-refinement. Extensive experiments demonstrate that LatentMorph **(I)** enhances the base model Janus-Pro by 16% on GenEval and 25% on T2I-CompBench; **(II)** outperforms explicit paradigms (*e.g.*, TwiG) by 15% and 11% on abstract reasoning tasks like WISE and IPV-Txt, **(III)** while reducing inference time by 44% and token consumption by 51%; and **(IV)** exhibits 71% cognitive alignment with human intuition on reasoning invocation.

Poster
GeoLoom: High-quality Geometric Diagram Generation from Textual Input

Xiaojing Wei, Ting Zhang, Wei He, Jingdong Wang, Hua Huang

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High-quality geometric diagram generation presents both a challenge and an opportunity: it demands strict spatial accuracy while offering well-defined constraints to guide generation. Inspired by recent advances in geometry problem solving that employ formal languages and symbolic solvers for enhanced correctness and interpretability, we propose GeoLoom, a novel framework for text-to-diagram generation in geometric domains. GeoLoom comprises two core components: an autoformalization module that translates natural language into a specifically designed generation-oriented formal language GeoLingua, and a coordinate solver that maps formal constraints to precise coordinates using the efficient Monte Carlo optimization. To support this framework, we introduce GeoNF, a dataset aligning natural language geometric descriptions with formal GeoLingua descriptions. We further propose a constraint-based evaluation metric that quantifies structural deviation, offering mathematically grounded supervision for iterative refinement. Empirical results demonstrate that GeoLoom significantly outperforms state-of-the-art baselines in structural fidelity, providing a principled foundation for interpretable and scalable diagram generation.

Poster