Test-Time Scaling in Multimodal Foundation Models: A Comprehensive Survey of Generation and Reasoning

Test-time Scaling (TTS) has emerged as a pivotal research direction for enhancing model performance by dynamically allocating computational resources during inference. Recent advancements have adapted this paradigm to Multimodal Foundation Models (MFMs), unlocking their potential in multimodal reasoning and generation. Despite rapid progress, the field lacks a systematic survey and unified theoretical framework to delineate the developmental landscape of multimodal TTS. To bridge this gap, we present the first comprehensive review of TTS research for MFMs, proposing a unified taxonomic framework that categorizes existing methodologies into three distinct strategies: sampling-based, feedback-based, and search-based approaches. We further summarize representative applications and benchmarks commonly utilized to evaluate multimodal TTS capabilities in generation and reasoning tasks. Finally, this survey discusses open challenges and outlines future research directions, providing a systematic roadmap for subsequent studies in this rapidly evolving field.

From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data

Geometric analysis fundamentally distinguishes between \textit{extrinsic} and \textit{intrinsic} perspectives. The dominant paradigm in current 3D representation learning relies on either extrinsic spatial structures or high-level semantics, struggling to capture the essence of shape identity and underlying manifold topology. To bridge this gap, we introduce a novel 3D representation learning paradigm, namely \textbf{PRISM}, for \textbf{P}re-training, which learns isometric embeddings by \textbf{R}ecovering the \textbf{I}ntrinsic \textbf{S}urface geodesic \textbf{M}etric. PRISM incorporates a topology-enforcing objective that explicitly constrains the structure of latent space, alongside a specialized two-stage training recipe mitigating sample imbalance inherent in the distribution of geodesic distances. Experiments demonstrate that our approach shows satisfactory accuracy, robustness, and high efficiency in geodesic distance prediction and achieves superior performance across diverse downstream tasks, including shape recognition, surface parameterization, and non-rigid correspondence. The code will be publicly available at https://github.com/AidenZhao/PRISM.

Underwater360: Reconstructing Underwater Scenes from Panoramic Images with Omnidirectional Gaussian Splatting

Underwater scene reconstruction is essential for immersive exploration of aquatic environments, yet remains challenging due to complex participating-media effects such as absorption and scattering, as well as the limited field of view (FoV) of conventional cameras. Although combining panoramic imaging with 3D Gaussian Splatting (3DGS) offers a promising direction for photorealistic underwater rendering, traditional 3DGS struggles with both spherical projection distortion and underwater medium degradation. In this paper, we propose \textbf{Underwater360}, a physics-informed omnidirectional 3DGS framework for underwater panoramic scene reconstruction. First, we introduce an Omnidirectional Gaussian Splatting module that performs ray casting directly in spherical camera space instead of relying on 2D projection approximations, thereby reducing geometric distortions under 360$^\circ$ FoV. Second, we design a physics-based appearance-medium modeling architecture with pose-conditioned appearance embeddings to explicitly decouple intrinsic scene radiance from depth-dependent backscatter and attenuation, enabling physically grounded scene appearance restoration. Finally, we establish a new panoramic underwater benchmark dataset containing both synthetic and real-world scenes. Extensive experiments demonstrate that Underwater360 achieves superior performance in underwater novel view synthesis and scene appearance restoration, delivering improved rendering quality and cross-view consistency in complex underwater environments. The code and datasets are released at https://github.com/SwcK423/Underwater360

Metric--Phase Fields: Decoupling Distance and Sign for Thin-Structure Reconstruction from Unoriented Point Clouds

Neural Signed Distance Functions (SDFs) excel at reconstructing watertight manifolds but fail on thin structures and open boundaries due to strict inside--outside constraints. Conversely, Unsigned Distance Fields (UDFs) accommodate general geometries but suffer from gradient singularities at the zero-level set, hindering optimization and extraction. We introduce Metric--Phase Fields (MPFs), a decoupled implicit representation that separates metric proximity from topological phase. Given an unoriented point cloud, MPFs learn (i) an unsigned metric field $r$ and (ii) a smooth phase field $θ$, for which we derive a bounded phase indicator $P=\tanh(βθ)$ that provides soft inside--outside cues where they are meaningful. We couple the two fields via a gated-metric formulation with a residual phase injection to obtain a signed implicit function with stable near-surface gradients. The phase coefficient $β$ is learnable, allowing MPFs to adaptively control the sharpness of the phase transition and the degree of saturation of the soft sign indicator. Experiments on both synthetic and scanned thin-shell and thin-plate shapes demonstrate that MPFs preserve thin and layered structures more faithfully than recent SDF-based methods, while also enabling more robust training and more reliable surface extraction than UDF-based approaches. Check out \href{https://github.com/JIAYI-Scarlett/ICML2026-MPF}{MPFs-GitHub} for source code and test models.

Denoising-GS: Gaussian Splatting with Spatial-aware Denoising

Recent advances in 3D Gaussian Splatting (3DGS) have achieved remarkable success in high-fidelity Novel View Synthesis (NVS), yet the optimization process inevitably introduces noisy Gaussian primitives due to the sparse and incomplete initialization from Structure-from-Motion (SfM) point clouds. Most existing methods focus solely on adjusting the positions of primitives during optimization, while neglecting the underlying spatial structure. To this end, we introduce a new perspective by formulating the optimization of 3DGS as a primitive denoising process and propose Denoising-GS, a spatial-aware denoising framework for Gaussian primitives by taking both the positions and spatial structure into consideration. Specifically, we design an optimizer that preserves the spatial optimization flow of primitives, facilitating coherent and directed denoising rather than random perturbations. Building upon this, the Spatial Gradient-based Denoising strategy jointly considers the spatial supports of primitives to ensure gradient-consistent updates. Furthermore, the Uncertainty-based Denoising module estimates primitive-wise uncertainty to prune redundant or noisy primitives, while the Spatial Coherence Refinement strategy selectively splits primitives in sparse regions to maintain structural completeness. Experiments conducted on three benchmark datasets demonstrate that Denoising-GS consistently enhances NVS fidelity while maintaining representation compactness, achieving state-of-the-art performance across all benchmarks. Source code and models will be made publicly available.

OCP: Orthogonal Constrained Projection for Sparse Scaling in Industrial Commodity Recommendation

In industrial commodity recommendation systems, the representation quality of Item-Id vocabularies directly impacts the scalability and generalization ability of recommendation models. A key challenge is that traditional Item-Id vocabularies, when subjected to sparse scaling, suffer from low-frequency information interference, which restricts their expressive power for massive item sets and leads to representation collapse. To address this issue, we propose an Orthogonal Constrained Projection method to optimize embedding representation. By enforcing orthogonality, the projection constrains the backpropagation manifold, aligning the singular value spectrum of the learned embeddings with the orthogonal basis. This alignment ensures high singular entropy, thereby preserving isotropic generalized features while suppressing spurious correlations and overfitting to rare items. Empirical results demonstrate that OCP accelerates loss convergence and enhances the model's scalability; notably, it enables consistent performance gains when scaling up dense layers. Large-scale industrial deployment on JD.com further confirms its efficacy, yielding a 12.97% increase in UCXR and an 8.9% uplift in GMV, highlighting its robust utility for scaling up both sparse vocabularies and dense architectures.

Multilingual AI-Driven Password Strength Estimation with Similarity-Based Detection

Considering the rise of cyberattacks incidents worldwide, the need to ensure stronger passwords is necessary. Developing a password strength meter (PSM) can help users create stronger passwords when creating an account on an online platform. This research aimed to explore whether incorporating a non-English training dataset (specifically Indian) can improve the performance of a PSM. Findings show that PSMs can be improved by utilising learning of words from other languages. Another contribution of the research was to compare and provide an analysis of AI generated data (specifically by ChatGPT) and PassGAN (existing state-of-the-art model), proving that PassGAN-like tools may no longer be needed as the performance is higher using AI generated data. To further strengthen detection, a Jaro similarity-based matching mechanism was incorporated, enabling the classification of passwords that are highly similar to known weak passwords - this addresses limitations of direct matching techniques used in prior work. A final novel contribution is on developing a PSM tailored for Indian passwords, which has not been developed previously - this resulted in a near-perfect matching accuracy using a Jaro function value of 0.5. Although performance improvements were constrained by limited data and training, results suggest that using the ChatGPT dataset is a viable and effective strategy for developing secure, language-aware password strength meters.

LFPO: Likelihood-Free Policy Optimization for Masked Diffusion Models

Reinforcement Learning with Verifiable Rewards (RLVR) has achieved remarkable success in improving autoregressive models, especially in domains requiring correctness like mathematical reasoning and code generation. However, directly applying such paradigms to Diffusion Large Language Models (dLLMs) is fundamentally hindered by the intractability of exact likelihood computation, which forces existing methods to rely on high-variance approximations. To bridge this gap, we propose Likelihood-Free Policy Optimization (LFPO), a native framework that maps the concept of vector field flow matching to the discrete token space. Specifically, LFPO formulates alignment as geometric velocity rectification, which directly optimizes denoising logits via contrastive updates. This design effectively bypasses the errors inherent in likelihood approximation, yielding the precise gradient estimation. Furthermore, LFPO enforce consistency by predicting final solutions from intermediate steps, effectively straightening the probability flow to enable high-quality generation with significantly fewer iterations. Extensive experiments demonstrate that LFPO not only outperforms state-of-the-art baselines on code and reasoning benchmarks but also accelerates inference by approximately 20% through reduced diffusion steps.

Words & Weights: Streamlining Multi-Turn Interactions via Co-Adaptation

Test-time policy adaptation for multi-turn interactions (T2PAM) is essential for aligning Large Language Models (LLMs) with dynamic user needs during inference time. However, existing paradigms commonly treat test-time adaptation as a single-axis problem, either purely refining instructions (Prompt Engineering) or only adjusting weights (Test-Time Training), ignoring that interaction failures stem from a coupled mix of ambiguity and incapacity. We argue that these two optimization paths are not merely additive but synergistic: semantic clarity acts as a pre-conditioner for effective parameter updates. To this end, we propose ROSA2, a framework that reformulates interaction as a joint optimization problem over the heterogeneous space of Words and Weights. By mathematically decomposing the error signal, ROSA2 utilizes textual gradients to rectify intent ambiguity and parameter updates to bridge capability gaps. Theoretically, we prove that this co-adaptation strictly reduces the required parameter shift for convergence. Empirically, ROSA2 outperforms state-of-the-art baselines by 30% on MATH while reducing interaction turns by 40%, demonstrating that refining the context unlocks the true potential of parameter updates.

VAGNet: Grounding 3D Affordance from Human-Object Interactions in Videos

3D object affordance grounding aims to identify regions on 3D objects that support human-object interaction (HOI), a capability essential to embodied visual reasoning. However, most existing approaches rely on static visual or textual cues, neglecting that affordances are inherently defined by dynamic actions. As a result, they often struggle to localize the true contact regions involved in real interactions. We take a different perspective. Humans learn how to use objects by observing and imitating actions, not just by examining shapes. Motivated by this intuition, we introduce video-guided 3D affordance grounding, which leverages dynamic interaction sequences to provide functional supervision. To achieve this, we propose VAGNet, a framework that aligns video-derived interaction cues with 3D structure to resolve ambiguities that static cues cannot address. To support this new setting, we introduce PVAD, the first HOI video-3D pairing affordance dataset, providing functional supervision unavailable in prior works. Extensive experiments on PVAD show that VAGNet achieves state-of-the-art performance, significantly outperforming static-based baselines. The code and dataset will be open publicly.