Daily Papers

Augmenting large language models (LLMs) with auxiliary tokens has emerged as a promising strategy for enhancing model performance. In this work, we introduce a lightweight method termed latent tokens; these are dummy tokens that may be non-interpretable in natural language but steer the autoregressive decoding process of a Transformer-based LLM via the attention mechanism. The proposed latent tokens can be seamlessly integrated with a pre-trained Transformer, trained in a parameter-efficient manner, and applied flexibly at inference time, while adding minimal complexity overhead to the existing infrastructure of standard Transformers. We propose several hypotheses about the underlying mechanisms of latent tokens and design synthetic tasks accordingly to verify them. Numerical results confirm that the proposed method noticeably outperforms the baselines, particularly in the out-of-distribution generalization scenarios, highlighting its potential in improving the adaptability of LLMs.

Chain-of-Thought (CoT) prompting has improved the reasoning performance of large language models (LLMs), but it remains unclear why it works and whether it is the unique mechanism for triggering reasoning in large language models. In this work, we study this question by directly analyzing and intervening on the internal representations of LLMs with Sparse Autoencoders (SAEs), identifying a small set of latent features that are causally associated with LLM reasoning behavior. Across multiple model families and reasoning benchmarks, we find that steering a single reasoning-related latent feature can substantially improve accuracy without explicit CoT prompting. For large models, latent steering achieves performance comparable to standard CoT prompting while producing more efficient outputs. We further observe that this reasoning-oriented internal state is triggered early in generation and can override prompt-level instructions that discourage explicit reasoning. Overall, our results suggest that multi-step reasoning in LLMs is supported by latent internal activations that can be externally activated, while CoT prompting is one effective, but not unique, way of activating this mechanism rather than its necessary cause.

Looped Transformers scale latent computation by repeatedly applying shared blocks, but sequential looping increases latency and KV-cache memory with the loop count. Parallel loop Transformers (PLT) alleviate this cost through cross-loop position offsets (CLP) and shared-KV gated sliding-window attention, making loop count a practical design choice. We therefore study PLT loop-count selection through a gain--cost view: an extra loop may refine representations, but CLP also introduces a positional mismatch at each loop boundary. We instantiate this study by training LoopCoder-v2, a family of 7B PLT coders with different loop counts, from scratch on 18T tokens, followed by matched instruction tuning and evaluation. Empirically, the two-loop variant delivers broad gains over the non-looped baseline across code generation, code reasoning, agentic software engineering, and tool-use benchmarks, improving SWE-bench Verified from 43.0 to 64.4 points and Multi-SWE from 14.0 to 31.0 points. In contrast, variants with three or more loops regress, revealing a strongly non-monotonic loop-count effect. Our diagnostics show that loop 2 provides the main productive refinement, while later loops yield diminishing, oscillatory updates and reduced representational diversity. Because the CLP-induced mismatch remains roughly fixed as refinement gains shrink, the offset cost increasingly dominates. This gain--cost trade-off explains PLT's saturation at two loops and provides diagnostics for loop-count selection.

Universal multimodal embedding (UME) maps heterogeneous inputs into a shared retrieval space with a single model. Recent approaches improve UME by generating explicit chain-of-thought (CoT) rationales before extracting embeddings, enabling multimodal large language models to better infer complex query intent. However, explicit CoT incurs substantial inference overhead and can compress rich multimodal evidence into a narrow textual bottleneck. We propose PLUME, a latent reasoning framework that advances UME by replacing verbalized CoT with a short autoregressive rollout of continuous latent states. To support diverse multimodal queries, PLUME further introduces a semantic-anchor-guided transition adapter that steers latent rollout along different reasoning trajectories under the same fixed computation budget. To stabilize training, PLUME adopts a progressive explicit-to-latent curriculum that uses verbalized reasoning only as a temporary training scaffold and gradually transfers this behavior into hidden-state computation, eliminating explicit CoT at inference. On the 78-task MMEB-v2 benchmark, PLUME outperforms strong explicit-CoT UME baselines while reducing reasoning from hundreds of generated tokens to fewer than 10 latent steps, delivering over 30x faster inference. PLUME is especially well suited to retrieval settings where relevant evidence is dense, structurally complex, and difficult to organize through verbalized intermediate rationales, such as video and visual document retrieval. These results show that structured latent computation can preserve the benefits of intermediate reasoning without the overhead of explicit rationale generation, providing a stronger and more efficient paradigm for practical retrieval systems.

Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token generation by propagating continuous states, yet replacing explicit derivations with latent computation can hurt tasks that require symbolic checking. We propose Latent-Then-Explicit Reasoning (LaTER), a two-stage paradigm that first performs bounded exploration in a continuous latent space and then switches to explicit CoT for verification and answer generation. In a training-free instantiation, LaTER projects final-layer hidden states back to the input embedding space, preserves the latent KV cache, and uses entropy and model-native stop-token probes to decide when to switch. We find that strong reasoning models already exhibit structured latent trajectories under this interface. On Qwen3-14B, training-free LaTER reduces total token usage by 16%-32% on several benchmarks while matching or improving accuracy on most of them; for example, it improves AIME 2025 from 70.0% to 73.3% while reducing tokens from 15,730 to 10,661. We further construct Latent-Switch-69K, a supervised corpus that pairs condensed solution intuitions with shortened explicit derivations. Fine-tuning with latent rollout and halting supervision yields additional gains: trained LaTER reaches 80.0% accuracy on AIME 2025, 10.0 points above the standard CoT baseline, while using 33% fewer tokens. Our code, data, and model are available at https://github.com/TioeAre/LaTER.

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.

Latent chain-of-thought compresses reasoning by replacing visible reasoning traces with continuous hidden-state recurrence, but existing formulations are difficult to optimize with standard on-policy reinforcement learning (RL) and hard to interpret causally. Our key insight is that a single pair of explicit boundary tokens can address both issues at once: discrete entry and exit anchors make the latent block compatible with standard on-policy RL, and the same anchors offer a natural foothold for mechanistic analysis. Motivated by this, we propose SWITCH, a switchable latent reasoning framework. The model emits <swi> to enter latent mode and </swi> to exit. Because the boundaries are ordinary discrete tokens, the GRPO policy ratio is well-defined at every decision point. The same anchors also expose the latent steps to direct probing and causal intervention. We train the model with a visible-to-latent curriculum and a Switch-GRPO objective that propagates gradients through recurrent latent computation. SWITCH consistently outperforms prior hidden-state-recurrence latent reasoning approaches at similar scale. Mechanistic analysis through the boundary tokens further reveals three findings: (i) <swi> is a sharply localised, learned switching policy rather than a stylistic artefact; (ii) the latent step it opens performs problem-specific, causally important computation rather than acting as an inert placeholder; and (iii) that computation is concentrated at a single hidden-state transition on entry. Together, these results show that hidden-state-recurrence latent reasoning is both RL-trainable and open to direct mechanistic analysis, including of how on-policy RL itself improves the model from the inside.

Latent diffusion models have emerged as a leading paradigm for efficient video generation. However, as user expectations shift toward higher-resolution outputs, relying solely on latent computation becomes inadequate. A promising approach involves decoupling the process into two stages: semantic content generation and detail synthesis. The former employs a computationally intensive base model at lower resolutions, while the latter leverages a lightweight cascaded video super-resolution (VSR) model to achieve high-resolution output. In this work, we focus on studying key design principles for latter cascaded VSR models, which are underexplored currently. First, we propose two degradation strategies to generate training pairs that better mimic the output characteristics of the base model, ensuring alignment between the VSR model and its upstream generator. Second, we provide critical insights into VSR model behavior through systematic analysis of (1) timestep sampling strategies, (2) noise augmentation effects on low-resolution (LR) inputs. These findings directly inform our architectural and training innovations. Finally, we introduce interleaving temporal unit and sparse local attention to achieve efficient training and inference, drastically reducing computational overhead. Extensive experiments demonstrate the superiority of our framework over existing methods, with ablation studies confirming the efficacy of each design choice. Our work establishes a simple yet effective baseline for cascaded video super-resolution generation, offering practical insights to guide future advancements in efficient cascaded synthesis systems.

Chemical large language models (LLMs) predominantly rely on explicit Chain-of-Thought (CoT) in natural language to perform complex reasoning. However, chemical reasoning is inherently continuous and structural, and forcing it into discrete linguistic tokens introduces a fundamental representation mismatch that constrains both efficiency and performance. We introduce LatentChem, a latent reasoning interface that decouples chemical computation from textual generation, enabling models to perform multi-step reasoning directly in continuous latent space while emitting language only for final outputs. Remarkably, we observe a consistent emergent behavior: when optimized solely for task success, models spontaneously internalize reasoning, progressively abandoning verbose textual derivations in favor of implicit latent computation. This shift is not merely stylistic but computationally advantageous. Across diverse chemical reasoning benchmarks, LatentChem achieves a 59.88\% non-tie win rate over strong CoT-based baselines on ChemCoTBench, while delivering a 10.84times average inference speedup. Our results provide empirical evidence that chemical reasoning is more naturally and effectively realized as continuous latent dynamics rather than discretized linguistic trajectories.

Current transformers discard their rich latent residual stream between positions, reconstructing latent reasoning context at each new position and leaving potential reasoning capacity untapped. The State Stream Transformer (SST) V2 enables parameter-efficient reasoning in continuous latent space through an FFN-driven nonlinear recurrence at each decoder layer, where latent states are streamed horizontally across the full sequence via a learned blend. This same mechanism supports continuous latent deliberation per position at inference time, dedicating additional FLOPs to exploring abstract reasoning before committing to a token. A two-pass parallel training procedure resolves the sequential dependency of the recurrence to allow compute-efficient training. Hidden state analysis shows the state stream facilitates reasoning through exploration of distinct semantic basins in continuous latent space, where transitions at content-dependent positions move the model into a substantially different Bayesian posterior, directly influencing the latent space at future positions. We also find, via a learned probe, that at the first generated token position, the latent state already predicts whether the eventual answer will survive or break under additional latent computation for every subsequent position. Co-trained into an existing 27B backbone using only a small dataset of GSM8K examples, the SST delivers a +15.15 point gain over a fine-tuning-matched baseline on out-of-distribution GPQA-Diamond and cuts that same baseline's remaining GSM8K errors by 46%, together showing that the reasoning improvement is attributable to the architectural mechanism rather than scale or training data. On GPQA-Diamond, the resulting 27B SST also achieves higher accuracy than several larger open-weight and proprietary systems, including open-weight models up to 25 times larger.

Looped language models (LoopLMs) perform iterative latent computation to refine internal representations, offering a promising alternative to explicit chain-of-thought (CoT) reasoning. However, existing reinforcement learning (RL) paradigms primarily target output tokens, creating a structural mismatch with looped architectures whose reasoning unfolds implicitly. In this work, we propose LoopRPT, a reinforcement pre-training framework tailored for LoopLMs. By reframing next-token prediction as a next-token reasoning task, LoopRPT assigns reinforcement signals directly to latent steps using an EMA teacher reference and noisy latent rollouts. This formulation enables RL to directly shape intermediate representations, compressing effective reasoning into fewer iterations. We instantiate LoopRPT on the Ouro architecture across multiple model scales. Results demonstrate that LoopRPT consistently improves per-step representation quality, achieving Pareto dominance in accuracy-computation trade-offs. Notably, significant gains on hard tokens indicate that LoopRPT enhances early-stage reasoning rather than merely encouraging premature exits. Our findings highlight reinforcement pre-training as a principled paradigm for learning efficient latent reasoning in LoopLMs.

Large language models (LLMs) perform inference by following a fixed depth and order, non-recurrent execution of all layers. We reveal the wide existence of training-free, flexible, dynamic program-of-layers (PoLar), where pretrained layers can be packed as modules and then skipped or looped to form a customized program for each input. For most inputs, substantially shorter program executions can achieve the same or better accuracy, while incorrect predictions of the original LLM can be corrected by alternative programs with fewer layers. These observations indicate that inference admits multiple valid latent computations beyond the standard forward pass. To efficiently achieve PoLar in practice, we propose a lightweight PoLar prediction network, which learns to generate execution programs that dynamically skip or repeat pretrained layers for each input. Experiments on mathematical reasoning benchmarks demonstrate that PoLar consistently improves accuracy over standard inference and prior dynamic-depth methods, often while executing fewer layers, and that these gains persist under out-of-distribution evaluation. Our results suggest that fixed-depth execution captures only a narrow subset of an LLM's latent reasoning capacity.

While reasoning in LLMs plays a natural role in math, code generation, and multi-hop factual questions, its effect on simple, single-hop factual questions remains unclear. Such questions do not require step-by-step logical decomposition, making the utility of reasoning highly counterintuitive. Nevertheless, we find that enabling reasoning substantially expands the capability boundary of the model's parametric knowledge recall, unlocking correct answers that are otherwise effectively unreachable. Why does reasoning aid parametric knowledge recall when there are no complex reasoning steps to be done? To answer this, we design a series of hypothesis-driven controlled experiments, and identify two key driving mechanisms: (1) a computational buffer effect, where the model uses the generated reasoning tokens to perform latent computation independent of their semantic content; and (2) factual priming, where generating topically related facts acts as a semantic bridge that facilitates correct answer retrieval. Importantly, this latter generative self-retrieval mechanism carries inherent risks: we demonstrate that hallucinating intermediate facts during reasoning increases the likelihood of hallucinations in the final answer. Finally, we show that our insights can be harnessed to directly improve model accuracy by prioritizing reasoning trajectories that contain hallucination-free factual statements.

We present GeoTransolver, a Multiscale Geometry-Aware Physics Attention Transformer for CAE that replaces standard attention with GALE, coupling physics-aware self-attention on learned state slices with cross-attention to a shared geometry/global/boundary-condition context computed from multi-scale ball queries (inspired by DoMINO) and reused in every block. Implemented and released in NVIDIA PhysicsNeMo, GeoTransolver persistently projects geometry, global and boundary condition parameters into physical state spaces to anchor latent computations to domain structure and operating regimes. We benchmark GeoTransolver on DrivAerML, Luminary SHIFT-SUV, and Luminary SHIFT-Wing, comparing against Domino, Transolver (as released in PhysicsNeMo), and literature-reported AB-UPT, and evaluate drag/lift R2 and Relative L1 errors for field variables. GeoTransolver delivers better accuracy, improved robustness to geometry/regime shifts, and favorable data efficiency; we include ablations on DrivAerML and qualitative results such as contour plots and design trends for the best GeoTransolver models. By unifying multiscale geometry-aware context with physics-based attention in a scalable transformer, GeoTransolver advances operator learning for high-fidelity surrogate modeling across complex, irregular domains and non-linear physical regimes.

Large language models (LLMs) can perform reasoning computations both internally within their latent space and externally by generating explicit token sequences like chains of thought. Significant progress in enhancing reasoning abilities has been made by scaling test-time compute. However, understanding and quantifying model-internal reasoning abilities - the inferential "leaps" models make between individual token predictions - remains crucial. This study introduces a benchmark (n = 4,000 items) designed to quantify model-internal reasoning in different domains. We achieve this by having LLMs indicate the correct solution to reasoning problems not through descriptive text, but by selecting a specific language of their initial response token that is different from English, the benchmark language. This not only requires models to reason beyond their context window, but also to overrise their default tendency to respond in the same language as the prompt, thereby posing an additional cognitive strain. We evaluate a set of 18 LLMs, showing significant performance variations, with GPT-4.5 achieving the highest accuracy (74.7%), outperforming models like Grok-2 (67.2%), and Llama 3.1 405B (65.6%). Control experiments and difficulty scaling analyses suggest that while LLMs engage in internal reasoning, we cannot rule out heuristic exploitations under certain conditions, marking an area for future investigation. Our experiments demonstrate that LLMs can "think" via latent-space computations, revealing model-internal inference strategies that need further understanding, especially regarding safety-related concerns such as covert planning, goal-seeking, or deception emerging without explicit token traces.

Transformer LLMs have been shown to exhibit strong reasoning ability that scales with inference-time compute, most prominently through token-space "thinking" chains of thought. A growing line of work pushes extra computation into the model's latent space, which we term Auxiliary Latent-Space Computation (ALSC). Existing ALSC methods largely fall into three buckets: (i) token-mediated latent rollouts, (ii) residual/activation steering, and (iii) memory (KV) compression. An underexplored alternative is memory consolidation/reconsolidation, two processes in the brain that are responsible for stabilising newly formed memory traces, and, upon recall, transiently rendering established traces plastic such they can integrate new contextual information before restabilising. In Transformer LLMs, this can be seen as analogous to performing in-place rewrites of new KV segments, and rewrites of recalled past segments. In this work, we give a theoretical justification as to why memory (re)consolidation via KV cache rewrites is beneficial for improved reasoning. We do this through the lens of Information Bottleneck (IB) theory, which posits that model generalisation emerges from an optimal balance between input information compression and retention of predictive information in latent representations. We then introduce the Bottlenecked Transformer, which augments a backbone LLM with a Cache Processor, an auxiliary Transformer that performs periodic, non-causal, in-place KV rewrites at newline-delimited reasoning step boundaries. The Processor consolidates recently written KV entries and reconsolidates a small, top-k attention-selected set of prior entries. We evaluate our Bottlenecked Transformer architecture on math reasoning benchmarks. Our model sees consistent performance gains over vanilla Transformers and pause-token augmented baselines, with gains of up to +6.6pp for selected tasks/backbones.

Large language models (LLMs), despite strong performance on complex mathematical problems, exhibit systematic limitations in counting tasks. This issue arises from architectural limits of transformers, where counting is performed across layers, leading to degraded precision for larger counting problems due to depth constraints. To address this limitation, we propose a simple test-time strategy inspired by System-2 cognitive processes that decomposes large counting tasks into smaller, independent sub-problems that the model can reliably solve. We evaluate this approach using observational and causal mediation analyses to understand the underlying mechanism of this System-2-like strategy. Our mechanistic analysis identifies key components: latent counts are computed and stored in the final item representations of each part, transferred to intermediate steps via dedicated attention heads, and aggregated in the final stage to produce the total count. Experimental results demonstrate that this strategy enables LLMs to surpass architectural limitations and achieve high accuracy on large-scale counting tasks. This work provides mechanistic insight into System-2 counting in LLMs and presents a generalizable approach for improving and understanding their reasoning behavior.

Recursive or looped language models have recently emerged as a new scaling axis by iteratively refining the same model computation over latent states to deepen reasoning. We extend such scaling principle from a single model to multi-agent systems, and ask: Can agent collaboration itself be scaled through recursion? To this end, we introduce RecursiveMAS, a recursive multi-agent framework that casts the entire system as a unified latent-space recursive computation. RecursiveMAS connects heterogeneous agents as a collaboration loop through the lightweight RecursiveLink module, enabling in-distribution latent thoughts generation and cross-agent latent state transfer. To optimize our framework, we develop an inner-outer loop learning algorithm for iterative whole-system co-optimization through shared gradient-based credit assignment across recursion rounds. Theoretical analyses of runtime complexity and learning dynamics establish that RecursiveMAS is more efficient than standard text-based MAS and maintains stable gradients during recursive training. Empirically, we instantiate RecursiveMAS under 4 representative agent collaboration patterns and evaluate across 9 benchmarks spanning mathematics, science, medicine, search, and code generation. In comparison with advanced single/multi-agent and recursive computation baselines, RecursiveMAS consistently delivers an average accuracy improvement of 8.3%, together with 1.2times-2.4times end-to-end inference speedup, and 34.6%-75.6% token usage reduction. Code and Data are provided in https://recursivemas.github.io.

The stateless architecture of Large Language Models inherently lacks the mechanism to preserve dynamic context, compelling agents to redundantly reprocess history to maintain long-horizon autonomy. While latent memory offers a solution, current approaches are hindered by architectural segregation, relying on auxiliary encoders that decouple memory from the reasoning backbone. We propose FlashMem, a framework that distills intrinsic memory directly from transient reasoning states via computation reuse. Leveraging the property that internal representations uniquely encode input trajectories, FlashMem identifies the last hidden state as a sufficient statistic for the interaction history. This enables a Shared-KV Consolidator to synthesize memory by attending directly to the backbone's frozen cache, eliminating redundant re-parameterization. Furthermore, a parameter-free Cognitive Monitor leverages attention entropy to adaptively trigger consolidation only when high epistemic uncertainty is detected. Experiments demonstrate that FlashMem matches the performance of heavy baselines while reducing inference latency by 5 times, effectively bridging the gap between efficiency and persistent cognition.

Modern LLMs are trained to "think" primarily via explicit text generation, such as chain-of-thought (CoT), which defers reasoning to post-training and under-leverages pre-training data. We present and open-source Ouro, named after the recursive Ouroboros, a family of pre-trained Looped Language Models (LoopLM) that instead build reasoning into the pre-training phase through (i) iterative computation in latent space, (ii) an entropy-regularized objective for learned depth allocation, and (iii) scaling to 7.7T tokens. Ouro 1.4B and 2.6B models enjoy superior performance that match the results of up to 12B SOTA LLMs across a wide range of benchmarks. Through controlled experiments, we show this advantage stems not from increased knowledge capacity, but from superior knowledge manipulation capabilities. We also show that LoopLM yields reasoning traces more aligned with final outputs than explicit CoT. We hope our results show the potential of LoopLM as a novel scaling direction in the reasoning era. Our model could be found in: http://ouro-llm.github.io.

Current approaches for scaling inference-time compute in transformers rely on training them to emit explicit chain-of-thought tokens before producing an answer. While these methods are powerful, they are limited because they cannot be applied during pretraining and are limited to only serially-generated, natural-language verbalization to scale inference-time compute. In this work, we propose Thoughtbubbles, a transformer variant that natively performs parallel adaptive computation in latent space by learning to fork or delete residual streams. Thus, tokens that require a large amount of computation can form a "bubble" of cloned residuals in the middle of the network for additional thinking. Crucially, this behavior is learned during pretraining with only language modeling loss. Thoughtbubbles outperforms both standard decoder LMs as well as non-adaptive parallel computation approaches on OpenWebText and peS2o perplexity and in zero-shot evaluations such as HellaSwag and LAMBADA after pretraining across 150M to 772M parameter scales. The implicit nature of our method enables adaptive computation to be learned starting at pretraining time, paving the way to unify train and test-time behavior for reasoning models.

Large Language Models (LLMs) have demonstrated strong generalization across a wide range of tasks. Reasoning with LLMs is central to solving multi-step problems and complex decision-making. To support efficient reasoning, recent studies have shifted attention from explicit chain-of-thought prompting toward implicit reasoning, where reasoning occurs silently via latent structures without emitting intermediate textual steps. Implicit reasoning brings advantages such as lower generation cost, faster inference, and better alignment with internal computation. Although prior surveys have discussed latent representations in the context of reasoning, a dedicated and mechanism-level examination of how reasoning unfolds internally within LLMs remains absent. This survey fills that gap by introducing a taxonomy centered on execution paradigms, shifting the focus from representational forms to computational strategies. We organize existing methods into three execution paradigms based on \textit{how and where internal computation unfolds}: latent optimization, signal-guided control, and layer-recurrent execution. We also review structural, behavioral and representation-based evidence that supports the presence of implicit reasoning in LLMs. We further provide a structured overview of the evaluation metrics and benchmarks used in existing works to assess the effectiveness and reliability of implicit reasoning. We maintain a continuously updated project at: https://github.com/digailab/awesome-llm-implicit-reasoning.

A unified foundation model for medical time series -- pretrained on open access and ethics board-approved medical corpora -- offers the potential to reduce annotation burdens, minimize model customization, and enable robust transfer across clinical institutions, modalities, and tasks, particularly in data-scarce or privacy-constrained environments. However, existing generalist time series foundation models struggle to handle medical time series data due to their inherent challenges, including irregular intervals, heterogeneous sampling rates, and frequent missing values. To address these challenges, we introduce MIRA, a unified foundation model specifically designed for medical time series forecasting. MIRA incorporates a Continuous-Time Rotary Positional Encoding that enables fine-grained modeling of variable time intervals, a frequency-specific mixture-of-experts layer that routes computation across latent frequency regimes to further promote temporal specialization, and a Continuous Dynamics Extrapolation Block based on Neural ODE that models the continuous trajectory of latent states, enabling accurate forecasting at arbitrary target timestamps. Pretrained on a large-scale and diverse medical corpus comprising over 454 billion time points collect from publicly available datasets, MIRA achieves reductions in forecasting errors by an average of 10% and 7% in out-of-distribution and in-distribution scenarios, respectively, when compared to other zero-shot and fine-tuned baselines. We also introduce a comprehensive benchmark spanning multiple downstream clinical tasks, establishing a foundation for future research in medical time series modeling.

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert space embeddings of POMDP where the feature of latent states and the feature of observations admit a conditional Hilbert space embedding of the observation emission process, and the latent state transition is deterministic. Under the function approximation setup where the optimal latent state-action Q-function is linear in the state feature, and the optimal Q-function has a gap in actions, we provide a computationally and statistically efficient algorithm for finding the exact optimal policy. We show our algorithm's computational and statistical complexities scale polynomially with respect to the horizon and the intrinsic dimension of the feature on the observation space. Furthermore, we show both the deterministic latent transitions and gap assumptions are necessary to avoid statistical complexity exponential in horizon or dimension. Since our guarantee does not have an explicit dependence on the size of the state and observation spaces, our algorithm provably scales to large-scale POMDPs.

Text analysis of social media for sentiment, topic analysis, and other analysis depends initially on the selection of keywords and phrases that will be used to create the research corpora. However, keywords that researchers choose may occur infrequently, leading to errors that arise from using small samples. In this paper, we use the capacity for memorization, interpolation, and extrapolation of Transformer Language Models such as the GPT series to learn the linguistic behaviors of a subgroup within larger corpora of Yelp reviews. We then use prompt-based queries to generate synthetic text that can be analyzed to produce insights into specific opinions held by the populations that the models were trained on. Once learned, more specific sentiment queries can be made of the model with high levels of accuracy when compared to traditional keyword searches. We show that even in cases where a specific keyphrase is limited or not present at all in the training corpora, the GPT is able to accurately generate large volumes of text that have the correct sentiment.

Sequential recommendation increasingly employs latent multi-step reasoning to enhance test-time computation. Despite empirical gains, existing approaches largely drive intermediate reasoning states via target-dominant objectives without imposing explicit feasibility constraints. This results in latent drift, where reasoning trajectories deviate into implausible regions. We argue that effective recommendation reasoning should instead be viewed as navigation on a collaborative manifold rather than free-form latent refinement. To this end, we propose ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph. ManCAR constructs a local intent prior from the collaborative neighborhood of a user's recent actions, represented as a distribution over the item simplex. During training, the model progressively aligns its latent predictive distribution with this prior, forcing the reasoning trajectory to remain within the valid manifold. At test time, reasoning proceeds adaptively until the predictive distribution stabilizes, avoiding over-refinement. We provide a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms. Experiments on seven benchmarks demonstrate that ManCAR consistently outperforms state-of-the-art baselines, achieving up to a 46.88% relative improvement w.r.t. NDCG@10. Our code is available at https://github.com/FuCongResearchSquad/ManCAR.

Generative models, from diffusion models to large language models, achieve remarkable performance but at a cost in training data orders of magnitude larger than what biological learners require. An alternative paradigm has emerged in which networks are trained to predict their own latent representations of related views or masked regions, as in data2vec and JEPA -- an idea related to predictive-coding accounts of the cortex. Despite strong empirical results, the theoretical understanding of these methods remains limited. Central questions include: by how much does latent prediction actually improve data efficiency? Is there a benefit to stacking such methods into multi-scale hierarchies? We answer both using as data a tractable probabilistic context-free grammar that captures the compositional structure of natural language and images. Such a grammar generates strings of visible tokens by recursively applying production rules along a tree of hidden symbols of depth L. For such data, supervised or token-level SSL require a number of samples exponential in L to recover the latent tree; we prove that latent prediction achieves this with a number of samples constant in L, up to logarithmic factors. We confirm this bound with (i) a hierarchical clustering algorithm, (ii) an end-to-end neural network whose predictor-clusterer modules predict their own latents at each level via gradient descent, and (iii) the first sample-complexity analysis of data2vec, which we show implicitly performs hierarchical latent prediction. This suggests that explicit stacking such as H-JEPA is largely redundant.

Natural data is redundant yet predominant architectures tile computation uniformly across their input and output space. We propose the Recurrent Interface Networks (RINs), an attention-based architecture that decouples its core computation from the dimensionality of the data, enabling adaptive computation for more scalable generation of high-dimensional data. RINs focus the bulk of computation (i.e. global self-attention) on a set of latent tokens, using cross-attention to read and write (i.e. route) information between latent and data tokens. Stacking RIN blocks allows bottom-up (data to latent) and top-down (latent to data) feedback, leading to deeper and more expressive routing. While this routing introduces challenges, this is less problematic in recurrent computation settings where the task (and routing problem) changes gradually, such as iterative generation with diffusion models. We show how to leverage recurrence by conditioning the latent tokens at each forward pass of the reverse diffusion process with those from prior computation, i.e. latent self-conditioning. RINs yield state-of-the-art pixel diffusion models for image and video generation, scaling to 1024X1024 images without cascades or guidance, while being domain-agnostic and up to 10X more efficient than 2D and 3D U-Nets.

Video world models that maintain 3D spatial consistency across generated frames typically rely on explicit point cloud memory constructed in RGB space. This design is both computationally expensive, requiring repeated rendering and VAE encoding, and inherently lossy, as the round trip through pixel space discards rich features of the learned latent representation. In this paper, we introduce latent spatial memory for video world models, a persistent 3D cache that stores scene information directly in the diffusion latent space, avoiding pixel-space reconstruction. Building on this, we propose Mirage, a latent-space spatial memory framework that constructs the memory by lifting latent tokens into 3D via depth-guided back-projection and queries it by synthesizing novel views through direct latent-space warping. This unified formulation eliminates both the information loss of pixel-space reconstruction and the computational burden of repeated encoding and rendering. Experiments show that latent spatial memory achieves up to 10.57times faster end-to-end video generation and 55times reduction in memory footprint relative to explicit 3D baselines. Leveraging the geometric prior of the diffusion model, Mirage attains state-of-the-art performance on WorldScore and strong reconstruction quality on RealEstate10K.

Large climate-model ensembles are computationally expensive; yet many downstream analyses would benefit from additional, statistically consistent realizations of spatiotemporal climate variables. We study a generative modeling approach for producing new realizations from a limited set of available runs by transferring structure learned across an ensemble. Using monthly near-surface temperature time series from ten independent reanalysis realizations (ERA5), we find that a vanilla conditional variational autoencoder (CVAE) trained jointly across realizations yields a fragmented latent space that fails to generalize to unseen ensemble members. To address this, we introduce a latent-constrained CVAE (LC-CVAE) that enforces cross-realization homogeneity of latent embeddings at a small set of shared geographic 'anchor' locations. We then use multi-output Gaussian process regression in the latent space to predict latent coordinates at unsampled locations in a new realization, followed by decoding to generate full time series fields. Experiments and ablations demonstrate (i) instability when training on a single realization, (ii) diminishing returns after incorporating roughly five realizations, and (iii) a trade-off between spatial coverage and reconstruction quality that is closely linked to the average neighbor distance in latent space.

Computational imaging methods increasingly rely on powerful generative diffusion models to tackle challenging image restoration tasks. In particular, state-of-the-art zero-shot image inverse solvers leverage distilled text-to-image latent diffusion models (LDMs) to achieve unprecedented accuracy and perceptual quality with high computational efficiency. However, extending these advances to high-definition video restoration remains a significant challenge, due to the need to recover fine spatial detail while capturing subtle temporal dependencies. Consequently, methods that naively apply image-based LDM priors on a frame-by-frame basis often result in temporally inconsistent reconstructions. We address this challenge by leveraging recent advances in Video Consistency Models (VCMs), which distill video latent diffusion models into fast generators that explicitly capture temporal causality. Building on this foundation, we propose LVTINO, the first zero-shot or plug-and-play inverse solver for high definition video restoration with priors encoded by VCMs. Our conditioning mechanism bypasses the need for automatic differentiation and achieves state-of-the-art video reconstruction quality with only a few neural function evaluations, while ensuring strong measurement consistency and smooth temporal transitions across frames. Extensive experiments on a diverse set of video inverse problems show significant perceptual improvements over current state-of-the-art methods that apply image LDMs frame by frame, establishing a new benchmark in both reconstruction fidelity and computational efficiency.

Looped computation shows promise in improving the reasoning-oriented performance of LLMs by scaling test-time compute. However, existing approaches typically require either training recurrent models from scratch or applying disruptive retrofits, which involve substantial computational costs and may compromise pretrained capabilities. To address these limitations, we introduce Looped Depth Up-Scaling (LoopUS), a post-training framework that converts a standard pretrained LLM into a looped architecture. As a key technical contribution, LoopUS recasts the pretrained LLM into an encoder, a looped reasoning block, and a decoder. It operationalizes this latent-refinement architecture through four core components: (1) block decomposition, guided by staged representation dynamics; (2) an input-dependent selective gate to mitigate hidden-state drift; (3) random deep supervision for memory-efficient learning over long recursive horizons; and (4) a confidence head for adaptive early exiting. Collectively, these mechanisms transform a standard non-looped model into a looped form while stabilizing it against both computational bottlenecks and representation collapse. Through stable latent looping, LoopUS improves reasoning-oriented performance without extending the generated traces or requiring recurrent training from scratch. For more details, see https://thrillcrazyer.github.io/LoopUS

Recent advances in large language models (LLMs) have introduced latent reasoning as a promising alternative to autoregressive reasoning. By performing internal computation with hidden states from previous steps, latent reasoning benefit from more informative features rather than sampling a discrete chain-of-thought (CoT) path. Yet latent reasoning approaches are often incompatible with LLMs, as their continuous paradigm conflicts with the discrete nature of autoregressive generation. Moreover, these methods rely on CoT traces for training and thus fail to exploit the inherent reasoning patterns of LLMs. In this work, we explore latent reasoning by leveraging the intrinsic capabilities of LLMs via reinforcement learning (RL). To this end, we introduce hybrid reasoning policy optimization (HRPO), an RL-based hybrid latent reasoning approach that (1) integrates prior hidden states into sampled tokens with a learnable gating mechanism, and (2) initializes training with predominantly token embeddings while progressively incorporating more hidden features. This design maintains LLMs' generative capabilities and incentivizes hybrid reasoning using both discrete and continuous representations. In addition, the hybrid HRPO introduces stochasticity into latent reasoning via token sampling, thereby enabling RL-based optimization without requiring CoT trajectories. Extensive evaluations across diverse benchmarks show that HRPO outperforms prior methods in both knowledge- and reasoning-intensive tasks. Furthermore, HRPO-trained LLMs remain interpretable and exhibit intriguing behaviors like cross-lingual patterns and shorter completion lengths, highlighting the potential of our RL-based approach and offer insights for future work in latent reasoning.

Diffusion models have been widely adopted in image generation, producing higher-quality and more diverse samples than generative adversarial networks (GANs). We introduce a latent diffusion model (LDM) for precipitation nowcasting - short-term forecasting based on the latest observational data. The LDM is more stable and requires less computation to train than GANs, albeit with more computationally expensive generation. We benchmark it against the GAN-based Deep Generative Models of Rainfall (DGMR) and a statistical model, PySTEPS. The LDM produces more accurate precipitation predictions, while the comparisons are more mixed when predicting whether the precipitation exceeds predefined thresholds. The clearest advantage of the LDM is that it generates more diverse predictions than DGMR or PySTEPS. Rank distribution tests indicate that the distribution of samples from the LDM accurately reflects the uncertainty of the predictions. Thus, LDMs are promising for any applications where uncertainty quantification is important, such as weather and climate.

Latent space is rapidly emerging as a native substrate for language-based models. While modern systems are still commonly understood through explicit token-level generation, an increasing body of work shows that many critical internal processes are more naturally carried out in continuous latent space than in human-readable verbal traces. This shift is driven by the structural limitations of explicit-space computation, including linguistic redundancy, discretization bottlenecks, sequential inefficiency, and semantic loss. This survey aims to provide a unified and up-to-date landscape of latent space in language-based models. We organize the survey into five sequential perspectives: Foundation, Evolution, Mechanism, Ability, and Outlook. We begin by delineating the scope of latent space, distinguishing it from explicit or verbal space and from the latent spaces commonly studied in generative visual models. We then trace the field's evolution from early exploratory efforts to the current large-scale expansion. To organize the technical landscape, we examine existing work through the complementary lenses of mechanism and ability. From the perspective of Mechanism, we identify four major lines of development: Architecture, Representation, Computation, and Optimization. From the perspective of Ability, we show how latent space supports a broad capability spectrum spanning Reasoning, Planning, Modeling, Perception, Memory, Collaboration, and Embodiment. Beyond consolidation, we discuss the key open challenges, and outline promising directions for future research. We hope this survey serves not only as a reference for existing work, but also as a foundation for understanding latent space as a general computational and systems paradigm for next-generation intelligence.

The steep computational cost of diffusion models at inference hinders their use as fast physics emulators. In the context of image and video generation, this computational drawback has been addressed by generating in the latent space of an autoencoder instead of the pixel space. In this work, we investigate whether a similar strategy can be effectively applied to the emulation of dynamical systems and at what cost. We find that the accuracy of latent-space emulation is surprisingly robust to a wide range of compression rates (up to 1000x). We also show that diffusion-based emulators are consistently more accurate than non-generative counterparts and compensate for uncertainty in their predictions with greater diversity. Finally, we cover practical design choices, spanning from architectures to optimizers, that we found critical to train latent-space emulators.

Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges, particularly on consumer-grade hardware. This paper introduces an innovative approach for the parametric and practical compression of LLMs based on reduced order modelling, which entails low-rank decomposition within the feature space and re-parameterization in the weight space. Notably, this compression technique operates in a layer-wise manner, obviating the need for a GPU device and enabling the compression of billion-scale models within stringent constraints of both memory and time. Our method represents a significant advancement in model compression by leveraging matrix decomposition, demonstrating superior efficacy compared to the prevailing state-of-the-art structured pruning method.

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.

While Large Language Models (LLMs) demonstrate exceptional performance in surface-level text generation, their nature in handling complex multi-step reasoning tasks often remains one of ``statistical fitting'' rather than systematic logical deduction. Traditional Reinforcement Learning (RL) attempts to mitigate this by introducing a ``think-before-speak'' paradigm. However, applying RL directly in high-dimensional, discrete token spaces faces three inherent challenges: sample-inefficient rollouts, high gradient estimation variance, and the risk of catastrophic forgetting. To fundamentally address these structural bottlenecks, we propose DeepLatent Reasoning (DLR), a latent-space bidirectional contrastive reinforcement learning framework. This framework shifts the trial-and-error cost from expensive token-level full sequence generation to the continuous latent manifold. Specifically, we introduce a lightweight assistant model to efficiently sample K reasoning chain encodings within the latent space. These encodings are filtered via a dual reward mechanism based on correctness and formatting; only high-value latent trajectories are fed into a frozen main model for single-pass decoding. To maximize reasoning diversity while maintaining coherence, we design a contrastive learning objective to enable directed exploration within the latent space. Since the main model parameters remain frozen during optimization, this method mathematically eliminates catastrophic forgetting. Experiments demonstrate that under comparable GPU computational budgets, DLR achieves more stable training convergence, supports longer-horizon reasoning chains, and facilitates the sustainable accumulation of reasoning capabilities, providing a viable path toward reliable and scalable reinforcement learning for LLMs.

We introduce Motion2VecSets, a 4D diffusion model for dynamic surface reconstruction from point cloud sequences. While existing state-of-the-art methods have demonstrated success in reconstructing non-rigid objects using neural field representations, conventional feed-forward networks encounter challenges with ambiguous observations from noisy, partial, or sparse point clouds. To address these challenges, we introduce a diffusion model that explicitly learns the shape and motion distribution of non-rigid objects through an iterative denoising process of compressed latent representations. The diffusion-based priors enable more plausible and probabilistic reconstructions when handling ambiguous inputs. We parameterize 4D dynamics with latent sets instead of using global latent codes. This novel 4D representation allows us to learn local shape and deformation patterns, leading to more accurate non-linear motion capture and significantly improving generalizability to unseen motions and identities. For more temporally-coherent object tracking, we synchronously denoise deformation latent sets and exchange information across multiple frames. To avoid computational overhead, we designed an interleaved space and time attention block to alternately aggregate deformation latents along spatial and temporal domains. Extensive comparisons against state-of-the-art methods demonstrate the superiority of our Motion2VecSets in 4D reconstruction from various imperfect observations. More detailed information can be found at https://vveicao.github.io/projects/Motion2VecSets/.

Large language models often improve reasoning by generating explicit chain-of-thought (CoT), demonstrating the importance of intermediate computation. However, textual CoT forces this computation through a discrete, serial, and communication-oriented token stream: each reasoning step must be verbalized before the model can proceed, even when the underlying update is semantic, uncertain, or only partially formed. Latent reasoning offers a higher-bandwidth alternative by performing intermediate computation in compact continuous states before committing to text. Yet existing latent-reasoning methods often sacrifice key advantages that make CoT effective in autoregressive language models, including native left-to-right generation, probabilistic sampling, compatibility with KV-cache decoding, and tractable likelihood estimation. We propose NF-CoT, a latent reasoning framework that preserves these advantages by modeling continuous thoughts with normalizing flows. NF-CoT instantiates a TARFlow-style normalizing flow inside the LLM backbone, defining a tractable probability model over compact continuous thoughts distilled from explicit CoT. Continuous-thought positions are generated by an NF head, while text positions are generated by the standard LM head within the same causal stream. This design provides exact likelihoods for latent thoughts, enables probabilistic left-to-right decoding with the original KV cache, and supports direct policy-gradient optimization in the latent reasoning space. On code-generation benchmarks, NF-CoT improves pass rates over explicit-CoT and prior latent-reasoning baselines while substantially reducing intermediate-reasoning cost.

Latent diffusion models excel at generating high-quality images but lose the benefits of end-to-end modeling. They discard information during image encoding, require a separately trained decoder, and model an auxiliary distribution to the raw data. In this paper, we propose Latent Forcing, a simple modification to existing architectures that achieves the efficiency of latent diffusion while operating on raw natural images. Our approach orders the denoising trajectory by jointly processing latents and pixels with separately tuned noise schedules. This allows the latents to act as a scratchpad for intermediate computation before high-frequency pixel features are generated. We find that the order of conditioning signals is critical, and we analyze this to explain differences between REPA distillation in the tokenizer and the diffusion model, conditional versus unconditional generation, and how tokenizer reconstruction quality relates to diffusability. Applied to ImageNet, Latent Forcing achieves a new state-of-the-art for diffusion transformer-based pixel generation at our compute scale.

Latent Chain-of-Thought (Latent-CoT) aims to enable step-by-step computation without emitting long rationales, yet its mechanisms remain unclear. We study CODI, a continuous-thought teacher-student distillation model, on strictly sequential polynomial-iteration tasks. Using logit-lens decoding, linear probes, attention analysis, and activation patching, we localize intermediate-state representations and trace their routing to the final readout. On two- and three-hop tasks, CODI forms the full set of bridge states that become decodable across latent-thought positions, while the final input follows a separate near-direct route; predictions arise via late fusion at the end-of-thought boundary. For longer hop lengths, CODI does not reliably execute a full latent rollout, instead exhibiting a partial latent reasoning path that concentrates on late intermediates and fuses them with the last input at the answer readout position. Ablations show that this partial pathway can collapse under regime shifts, including harder optimization. Overall, we delineate when CODI-style latent-CoT yields faithful iterative computation versus compressed or shortcut strategies, and highlight challenges in designing robust latent-CoT objectives for sequential reasoning.

Recent vision-language-action (VLA) models built on pretrained vision-language models (VLMs) have demonstrated strong generalization across manipulation tasks. However, they remain constrained by a single-frame observation paradigm and cannot fully benefit from the motion information offered by aggregated multi-frame historical observations, as the large vision-language backbone introduces substantial computational cost and inference latency. We propose CronusVLA, a unified framework that extends single-frame VLA models to the multi-frame paradigm through an efficient post-training stage. CronusVLA comprises three key components: (1) single-frame pretraining on large-scale embodied datasets with autoregressive action tokens prediction, which establishes an embodied vision-language foundation; (2) multi-frame encoding, adapting the prediction of vision-language backbones from discrete action tokens to motion features during post-training, and aggregating motion features from historical frames into a feature chunking; (3) cross-frame decoding, which maps the feature chunking to accurate actions via a shared decoder with cross-attention. By reducing redundant token computation and caching past motion features, CronusVLA achieves efficient inference. As an application of motion features, we further propose an action adaptation mechanism based on feature-action retrieval to improve model performance during finetuning. CronusVLA achieves state-of-the-art performance on SimplerEnv with 70.9% success rate, and 12.7% improvement over OpenVLA on LIBERO. Real-world Franka experiments also show the strong performance and robustness.

Large-scale 3D generative models require substantial computational resources yet often fall short in capturing fine details and complex geometries at high resolutions. We attribute this limitation to the inefficiency of current representations, which lack the compactness required to model the generative models effectively. To address this, we introduce a novel approach called Wavelet Latent Diffusion, or WaLa, that encodes 3D shapes into wavelet-based, compact latent encodings. Specifically, we compress a 256^3 signed distance field into a 12^3 times 4 latent grid, achieving an impressive 2427x compression ratio with minimal loss of detail. This high level of compression allows our method to efficiently train large-scale generative networks without increasing the inference time. Our models, both conditional and unconditional, contain approximately one billion parameters and successfully generate high-quality 3D shapes at 256^3 resolution. Moreover, WaLa offers rapid inference, producing shapes within two to four seconds depending on the condition, despite the model's scale. We demonstrate state-of-the-art performance across multiple datasets, with significant improvements in generation quality, diversity, and computational efficiency. We open-source our code and, to the best of our knowledge, release the largest pretrained 3D generative models across different modalities.

The remarkable success of Chain-of-Thought (CoT), which enhances performance by scaling generation steps at test-time, inspires us to ask: can we leverage a similar scaling of computational steps during pretraining to improve the generation of each individual token? To address this, we propose a novel pre-training methodology: Pretraining Language Models with Latent Thoughts (PonderLM-2). Our approach pretrains a language model (LM) to first generate an intermediate latent thought-the last hidden state of the current position-which is then used as input to predict the actual subsequent token. This additional computational step enables the LM to refine its prediction within unconstrained continuous space. Our experiments demonstrate that, at an identical inference cost, a LM that generates one additional latent thought per token outperforms a standard model with double the parameters. For instance, our PonderLM-2-Pythia-1.4B, pretrained on 300B tokens from the Pile, significantly surpasses the vanilla Pythia-2.8B trained on the same data on both language modeling and a range of general downstream tasks. Furthermore, increasing the number of latent thoughts generated before each actual token-forming a chain analogous to CoT-consistently improves the model's performance.

High-resolution image synthesis remains a core challenge in generative modeling, particularly in balancing computational efficiency with the preservation of fine-grained visual detail. We present Latent Wavelet Diffusion (LWD), a lightweight framework that enables any latent diffusion model to scale to ultra-high-resolution image generation (2K to 4K) for free. LWD introduces three key components: (1) a scale-consistent variational autoencoder objective that enhances the spectral fidelity of latent representations; (2) wavelet energy maps that identify and localize detail-rich spatial regions within the latent space; and (3) a time-dependent masking strategy that focuses denoising supervision on high-frequency components during training. LWD requires no architectural modifications and incurs no additional computational overhead. Despite its simplicity, it consistently improves perceptual quality and reduces FID in ultra-high-resolution image synthesis, outperforming strong baseline models. These results highlight the effectiveness of frequency-aware, signal-driven supervision as a principled and efficient approach for high-resolution generative modeling.

The recent use of diffusion prior, enhanced by pre-trained text-image models, has markedly elevated the performance of image super-resolution (SR). To alleviate the huge computational cost required by pixel-based diffusion SR, latent-based methods utilize a feature encoder to transform the image and then implement the SR image generation in a compact latent space. Nevertheless, there are two major issues that limit the performance of latent-based diffusion. First, the compression of latent space usually causes reconstruction distortion. Second, huge computational cost constrains the parameter scale of the diffusion model. To counteract these issues, we first propose a frequency compensation module that enhances the frequency components from latent space to pixel space. The reconstruction distortion (especially for high-frequency information) can be significantly decreased. Then, we propose to use Sample-Space Mixture of Experts (SS-MoE) to achieve more powerful latent-based SR, which steadily improves the capacity of the model without a significant increase in inference costs. These carefully crafted designs contribute to performance improvements in largely explored 4x blind super-resolution benchmarks and extend to large magnification factors, i.e., 8x image SR benchmarks. The code is available at https://github.com/amandaluof/moe_sr.

Computational modeling of single-cell gene expression is crucial for understanding cellular processes, but generating realistic expression profiles remains a major challenge. This difficulty arises from the count nature of gene expression data and complex latent dependencies among genes. Existing generative models often impose artificial gene orderings or rely on shallow neural network architectures. We introduce a scalable latent diffusion model for single-cell gene expression data, which we refer to as scLDM, that respects the fundamental exchangeability property of the data. Our VAE uses fixed-size latent variables leveraging a unified Multi-head Cross-Attention Block (MCAB) architecture, which serves dual roles: permutation-invariant pooling in the encoder and permutation-equivariant unpooling in the decoder. We enhance this framework by replacing the Gaussian prior with a latent diffusion model using Diffusion Transformers and linear interpolants, enabling high-quality generation with multi-conditional classifier-free guidance. We show its superior performance in a variety of experiments for both observational and perturbational single-cell data, as well as downstream tasks like cell-level classification.

Cardiac Magnetic Resonance (CMR) imaging is a critical tool for diagnosing and managing cardiovascular disease, yet its utility is often limited by the sparse acquisition of 2D short-axis slices, resulting in incomplete volumetric information. Accurate 3D reconstruction from these sparse slices is essential for comprehensive cardiac assessment, but existing methods face challenges, including reliance on predefined interpolation schemes (e.g., linear or spherical), computational inefficiency, and dependence on additional semantic inputs such as segmentation labels or motion data. To address these limitations, we propose a novel Cardiac Latent Interpolation Diffusion (CaLID) framework that introduces three key innovations. First, we present a data-driven interpolation scheme based on diffusion models, which can capture complex, non-linear relationships between sparse slices and improves reconstruction accuracy. Second, we design a computationally efficient method that operates in the latent space and speeds up 3D whole-heart upsampling time by a factor of 24, reducing computational overhead compared to previous methods. Third, with only sparse 2D CMR images as input, our method achieves SOTA performance against baseline methods, eliminating the need for auxiliary input such as morphological guidance, thus simplifying workflows. We further extend our method to 2D+T data, enabling the effective modeling of spatiotemporal dynamics and ensuring temporal coherence. Extensive volumetric evaluations and downstream segmentation tasks demonstrate that CaLID achieves superior reconstruction quality and efficiency. By addressing the fundamental limitations of existing approaches, our framework advances the state of the art for spatio and spatiotemporal whole-heart reconstruction, offering a robust and clinically practical solution for cardiovascular imaging.

The ability to generate 3D multiphase microstructures on-demand with targeted attributes can greatly accelerate the design of advanced materials. Here, we present a conditional latent diffusion model (LDM) framework that rapidly synthesizes high-fidelity 3D multiphase microstructures tailored to user specifications. Using this approach, we generate diverse two-phase and three-phase microstructures at high resolution (volumes of 128 times 128 times 64 voxels, representing >10^6 voxels each) within seconds, overcoming the scalability and time limitations of traditional simulation-based methods. Key design features, such as desired volume fractions and tortuosities, are incorporated as controllable inputs to guide the generative process, ensuring that the output structures meet prescribed statistical and topological targets. Moreover, the framework predicts corresponding manufacturing (processing) parameters for each generated microstructure, helping to bridge the gap between digital microstructure design and experimental fabrication. While demonstrated on organic photovoltaic (OPV) active-layer morphologies, the flexible architecture of our approach makes it readily adaptable to other material systems and microstructure datasets. By combining computational efficiency, adaptability, and experimental relevance, this framework addresses major limitations of existing methods and offers a powerful tool for accelerated materials discovery.

We present a novel, training-free approach for textual editing of real images using diffusion models. Unlike prior methods that rely on computationally expensive finetuning, our approach leverages LAtent SPatial Alignment (LASPA) to efficiently preserve image details. We demonstrate how the diffusion process is amenable to spatial guidance using a reference image, leading to semantically coherent edits. This eliminates the need for complex optimization and costly model finetuning, resulting in significantly faster editing compared to previous methods. Additionally, our method avoids the storage requirements associated with large finetuned models. These advantages make our approach particularly well-suited for editing on mobile devices and applications demanding rapid response times. While simple and fast, our method achieves 62-71\% preference in a user-study and significantly better model-based editing strength and image preservation scores.

We study the problem of modeling a population of agents pursuing unknown goals subject to unknown computational constraints. In standard models of bounded rationality, sub-optimal decision-making is simulated by adding homoscedastic noise to optimal decisions rather than explicitly simulating constrained inference. In this work, we introduce a latent inference budget model (L-IBM) that models agents' computational constraints explicitly, via a latent variable (inferred jointly with a model of agents' goals) that controls the runtime of an iterative inference algorithm. L-IBMs make it possible to learn agent models using data from diverse populations of suboptimal actors. In three modeling tasks -- inferring navigation goals from routes, inferring communicative intents from human utterances, and predicting next moves in human chess games -- we show that L-IBMs match or outperform Boltzmann models of decision-making under uncertainty. Inferred inference budgets are themselves meaningful, efficient to compute, and correlated with measures of player skill, partner skill and task difficulty.

AI-generated content has attracted lots of attention recently, but photo-realistic video synthesis is still challenging. Although many attempts using GANs and autoregressive models have been made in this area, the visual quality and length of generated videos are far from satisfactory. Diffusion models have shown remarkable results recently but require significant computational resources. To address this, we introduce lightweight video diffusion models by leveraging a low-dimensional 3D latent space, significantly outperforming previous pixel-space video diffusion models under a limited computational budget. In addition, we propose hierarchical diffusion in the latent space such that longer videos with more than one thousand frames can be produced. To further overcome the performance degradation issue for long video generation, we propose conditional latent perturbation and unconditional guidance that effectively mitigate the accumulated errors during the extension of video length. Extensive experiments on small domain datasets of different categories suggest that our framework generates more realistic and longer videos than previous strong baselines. We additionally provide an extension to large-scale text-to-video generation to demonstrate the superiority of our work. Our code and models will be made publicly available.

The human intrinsic desire to pursue knowledge, also known as curiosity, is considered essential in the process of skill acquisition. With the aid of artificial curiosity, we could equip current techniques for control, such as Reinforcement Learning, with more natural exploration capabilities. A promising approach in this respect has consisted of using Bayesian surprise on model parameters, i.e. a metric for the difference between prior and posterior beliefs, to favour exploration. In this contribution, we propose to apply Bayesian surprise in a latent space representing the agent's current understanding of the dynamics of the system, drastically reducing the computational costs. We extensively evaluate our method by measuring the agent's performance in terms of environment exploration, for continuous tasks, and looking at the game scores achieved, for video games. Our model is computationally cheap and compares positively with current state-of-the-art methods on several problems. We also investigate the effects caused by stochasticity in the environment, which is often a failure case for curiosity-driven agents. In this regime, the results suggest that our approach is resilient to stochastic transitions.

Large Language Models (LLMs) apply uniform computation to all tokens, despite language exhibiting highly non-uniform information density. This token-uniform regime wastes capacity on locally predictable spans while under-allocating computation to semantically critical transitions. We propose Dynamic Large Concept Models (DLCM), a hierarchical language modeling framework that learns semantic boundaries from latent representations and shifts computation from tokens to a compressed concept space where reasoning is more efficient. DLCM discovers variable-length concepts end-to-end without relying on predefined linguistic units. Hierarchical compression fundamentally changes scaling behavior. We introduce the first compression-aware scaling law, which disentangles token-level capacity, concept-level reasoning capacity, and compression ratio, enabling principled compute allocation under fixed FLOPs. To stably train this heterogeneous architecture, we further develop a decoupled μP parametrization that supports zero-shot hyperparameter transfer across widths and compression regimes. At a practical setting (R=4, corresponding to an average of four tokens per concept), DLCM reallocates roughly one-third of inference compute into a higher-capacity reasoning backbone, achieving a +2.69\% average improvement across 12 zero-shot benchmarks under matched inference FLOPs.

Diffusion transformers have emerged as an alternative to U-net-based diffusion models for high-fidelity image and video generation, offering superior scalability. However, their heavy computation remains a major obstacle to real-world deployment. Existing acceleration methods primarily exploit the temporal dimension such as reusing cached features across diffusion timesteps. Here, we propose Region-Adaptive Latent Upsampling (RALU), a training-free framework that accelerates inference along spatial dimension. RALU performs mixed-resolution sampling across three stages: 1) low-resolution denoising latent diffusion to efficiently capture global semantic structure, 2) region-adaptive upsampling on specific regions prone to artifacts at full-resolution, and 3) all latent upsampling at full-resolution for detail refinement. To stabilize generations across resolution transitions, we leverage noise-timestep rescheduling to adapt the noise level across varying resolutions. Our method significantly reduces computation while preserving image quality by achieving up to 7.0times speed-up on FLUX and 3.0times on Stable Diffusion 3 with minimal degradation. Furthermore, RALU is complementary to existing temporal accelerations such as caching methods, thus can be seamlessly integrated to further reduce inference latency without compromising generation quality.

Capturing complex user preferences from sparse behavioral sequences remains a fundamental challenge in sequential recommendation. Recent latent reasoning methods have shown promise by extending test-time computation through multi-step reasoning, yet they exclusively rely on depth-level scaling along a single trajectory, suffering from diminishing returns as reasoning depth increases. To address this limitation, we propose Parallel Latent Reasoning (PLR), a novel framework that pioneers width-level computational scaling by exploring multiple diverse reasoning trajectories simultaneously. PLR constructs parallel reasoning streams through learnable trigger tokens in continuous latent space, preserves diversity across streams via global reasoning regularization, and adaptively synthesizes multi-stream outputs through mixture-of-reasoning-streams aggregation. Extensive experiments on three real-world datasets demonstrate that PLR substantially outperforms state-of-the-art baselines while maintaining real-time inference efficiency. Theoretical analysis further validates the effectiveness of parallel reasoning in improving generalization capability. Our work opens new avenues for enhancing reasoning capacity in sequential recommendation beyond existing depth scaling.

Program synthesis methods aim to automatically generate programs restricted to a language that can explain a given specification of input-output pairs. While purely symbolic approaches suffer from a combinatorial search space, recent methods leverage neural networks to learn distributions over program structures to narrow this search space significantly, enabling more efficient search. However, for challenging problems, it remains difficult to train models to perform program synthesis in one shot, making test-time search essential. Most neural methods lack structured search mechanisms during inference, relying instead on stochastic sampling or gradient updates, which can be inefficient. In this work, we propose the Latent Program Network (LPN), a general algorithm for program induction that learns a distribution over latent programs in a continuous space, enabling efficient search and test-time adaptation. We explore how to train these networks to optimize for test-time computation and demonstrate the use of gradient-based search both during training and at test time. We evaluate LPN on ARC-AGI, a program synthesis benchmark that evaluates performance by generalizing programs to new inputs rather than explaining the underlying specification. We show that LPN can generalize beyond its training distribution and adapt to unseen tasks by utilizing test-time computation, outperforming algorithms without test-time adaptation mechanisms.

Unified models (UMs) hold promise for their ability to understand and generate content across heterogeneous modalities. Compared to merely generating visual content, the use of UMs for interleaved cross-modal reasoning is more promising and valuable, e.g., for solving understanding problems that require dense visual thinking, improving visual generation through self-reflection, or modeling visual dynamics of the physical world guided by stepwise action interventions. However, existing UMs necessitate pixel decoding as a bridge due to their disjoint visual representations for understanding and generation, which is both ineffective and inefficient. In this paper, we introduce LatentUM, a novel unified model that represents all modalities within a shared semantic latent space, eliminating the need for pixel-space mediation between visual understanding and generation. This design naturally enables flexible interleaved cross-modal reasoning and generation. Beyond improved computational efficiency, the shared representation substantially alleviates codec bias and strengthens cross-modal alignment, allowing LatentUM to achieve state-of-the-art performance on the Visual Spatial Planning benchmark, push the limits of visual generation through self-reflection, and support world modeling by predicting future visual states within the shared semantic latent space.

This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors. Our method first pretrains a flow model on the target features to capture the underlying distribution. This fixed flow model subsequently regularizes the latent space via an alignment loss, which reformulates the flow matching objective to treat the latents as optimization targets. We formally prove that minimizing this alignment loss establishes a computationally tractable surrogate objective for maximizing a variational lower bound on the log-likelihood of latents under the target distribution. Notably, the proposed method eliminates computationally expensive likelihood evaluations and avoids ODE solving during optimization. As a proof of concept, we demonstrate in a controlled setting that the alignment loss landscape closely approximates the negative log-likelihood of the target distribution. We further validate the effectiveness of our approach through large-scale image generation experiments on ImageNet with diverse target distributions, accompanied by detailed discussions and ablation studies. With both theoretical and empirical validation, our framework paves a new way for latent space alignment.

Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song et al.), we propose Latent Consistency Models (LCMs), enabling swift inference with minimal steps on any pre-trained LDMs, including Stable Diffusion (rombach et al). Viewing the guided reverse diffusion process as solving an augmented probability flow ODE (PF-ODE), LCMs are designed to directly predict the solution of such ODE in latent space, mitigating the need for numerous iterations and allowing rapid, high-fidelity sampling. Efficiently distilled from pre-trained classifier-free guided diffusion models, a high-quality 768 x 768 2~4-step LCM takes only 32 A100 GPU hours for training. Furthermore, we introduce Latent Consistency Fine-tuning (LCF), a novel method that is tailored for fine-tuning LCMs on customized image datasets. Evaluation on the LAION-5B-Aesthetics dataset demonstrates that LCMs achieve state-of-the-art text-to-image generation performance with few-step inference. Project Page: https://latent-consistency-models.github.io/

Current video generation models suffer from high computational latency, making real-time applications prohibitively costly. In this paper, we address this limitation by exploiting the temporal redundancy inherent in video latent patches. To this end, we propose the Latent Inter-frame Pruning with Attention Recovery (LIPAR) framework, which detects and skips recomputing duplicated latent patches. Additionally, we introduce a novel Attention Recovery mechanism that approximates the attention values of pruned tokens, thereby removing visual artifacts arising from naively applying the pruning method. Empirically, our method increases video editing throughput by 1.45times, on average achieving 12.2 FPS on an NVIDIA A6000 compared to the baseline 8.4 FPS. The proposed method does not compromise generation quality and can be seamlessly integrated with the model without additional training. Our approach effectively bridges the gap between traditional compression algorithms and modern generative pipelines.

Few-step image generation has seen rapid progress, with consistency and meanflow-based methods significantly reducing the number of sampling steps. Despite their low inference cost, these approaches often suffer from training instability and limited scalability. Sphere Encoder is a recent alternative that produces high-quality images in only a few steps; however, it requires repeated transitions between the pixel space and latent space during inference while jointly optimizing reconstruction and generation within a single architecture. This design leads to computational inefficiency and objective conflict between reconstruction and generation. To address these limitations, we decouple the framework into a fixed pretrained image encoder and a separate latent denoising model trained entirely in a spherical latent space. Our approach eliminates repeated pixel-space operations during training and inference, improving efficiency and allowing reconstruction and generation to specialize independently. On Animal-Faces, Oxford-Flowers and ImageNet-1K datasets, our method significantly outperforms Sphere Encoder in both generation quality and inference speed, while achieving competitive results against strong few-step and multi-step baselines.

Complex Reasoning in Large Language Models can be dynamically optimized using Test-Time Scaling (TTS) to mitigate Overthinking. Methods such as Coconut, SoftCoT and its variant are effective in continuous latent space inference, the core bottleneck still lies in the efficient generation and utilization of high-quality Latent Thought. Drawing from the theory of SoftCoT++ that a larger variance in the generated Latent Thought distribution more closely approximates the golden truth distribution, we propose a Latent Thought-Augmented Training Framework--LTA-Thinker, which improves distributional variance and enhances reasoning performance from two perspectives. First, LTA-Thinker constructs a Latent Thought generation architecture based on a learnable prior. This architecture aims to increase the variance distribution of generated Latent Thought Vectors in order to simplify the overall structure and raise the performance ceiling. Second, LTA-Thinker introduces a distribution-based directional optimization paradigm that jointly constrains both distribution locality and distribution scale. This mechanism improves information efficiency and computational cost through a multi-objective co-training strategy, which combines standard Supervised Fine-Tuning (SFT) loss with two novel losses: Semantic Alignment Loss, which utilizes KL divergence to ensure that the Latent Thought is highly relevant to the semantics of the question; Reasoning Focus Loss, which utilizes a contrastive learning mechanism to guide the model to focus on the most critical reasoning steps. Experiments show that LTA-thinker achieves state-of-the-art (SOTA) performance among various baselines and demonstrates a higher performance ceiling and better scaling effects.

Mixture of Experts (MoE) has emerged as a pivotal architectural paradigm for efficient scaling of Large Language Models (LLMs), operating through selective activation of parameter subsets for each input token. Nevertheless, conventional MoE architectures encounter substantial challenges, including excessive memory utilization and communication overhead during training and inference, primarily attributable to the proliferation of expert modules. In this paper, we introduce Mixture of Latent Experts (MoLE), a novel parameterization methodology that facilitates the mapping of specific experts into a shared latent space. Specifically, all expert operations are systematically decomposed into two principal components: a shared projection into a lower-dimensional latent space, followed by expert-specific transformations with significantly reduced parametric complexity. This factorized approach substantially diminishes parameter count and computational requirements. Beyond the pretraining implementation of the MoLE architecture, we also establish a rigorous mathematical framework for transforming pre-trained MoE models into the MoLE architecture, characterizing the sufficient conditions for optimal factorization and developing a systematic two-phase algorithm for this conversion process. Our comprehensive theoretical analysis demonstrates that MoLE significantly enhances computational efficiency across multiple dimensions while preserving model representational capacity. Empirical evaluations corroborate our theoretical findings, confirming that MoLE achieves performance comparable to standard MoE implementations while substantially reducing resource requirements.

We introduce nested diffusion models, an efficient and powerful hierarchical generative framework that substantially enhances the generation quality of diffusion models, particularly for images of complex scenes. Our approach employs a series of diffusion models to progressively generate latent variables at different semantic levels. Each model in this series is conditioned on the output of the preceding higher-level models, culminating in image generation. Hierarchical latent variables guide the generation process along predefined semantic pathways, allowing our approach to capture intricate structural details while significantly improving image quality. To construct these latent variables, we leverage a pre-trained visual encoder, which learns strong semantic visual representations, and modulate its capacity via dimensionality reduction and noise injection. Across multiple datasets, our system demonstrates significant enhancements in image quality for both unconditional and class/text conditional generation. Moreover, our unconditional generation system substantially outperforms the baseline conditional system. These advancements incur minimal computational overhead as the more abstract levels of our hierarchy work with lower-dimensional representations.

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods still face the challenges of expensive computing and a large number of function evaluations of off-the-shelf solvers in the pixel space. Furthermore, although latent-based generative methods have shown great success in recent years, this particular model type remains underexplored in this area. In this work, we propose to apply flow matching in the latent spaces of pretrained autoencoders, which offers improved computational efficiency and scalability for high-resolution image synthesis. This enables flow-matching training on constrained computational resources while maintaining their quality and flexibility. Additionally, our work stands as a pioneering contribution in the integration of various conditions into flow matching for conditional generation tasks, including label-conditioned image generation, image inpainting, and semantic-to-image generation. Through extensive experiments, our approach demonstrates its effectiveness in both quantitative and qualitative results on various datasets, such as CelebA-HQ, FFHQ, LSUN Church & Bedroom, and ImageNet. We also provide a theoretical control of the Wasserstein-2 distance between the reconstructed latent flow distribution and true data distribution, showing it is upper-bounded by the latent flow matching objective. Our code will be available at https://github.com/VinAIResearch/LFM.git.

Neural attention has become central to many state-of-the-art models in natural language processing and related domains. Attention networks are an easy-to-train and effective method for softly simulating alignment; however, the approach does not marginalize over latent alignments in a probabilistic sense. This property makes it difficult to compare attention to other alignment approaches, to compose it with probabilistic models, and to perform posterior inference conditioned on observed data. A related latent approach, hard attention, fixes these issues, but is generally harder to train and less accurate. This work considers variational attention networks, alternatives to soft and hard attention for learning latent variable alignment models, with tighter approximation bounds based on amortized variational inference. We further propose methods for reducing the variance of gradients to make these approaches computationally feasible. Experiments show that for machine translation and visual question answering, inefficient exact latent variable models outperform standard neural attention, but these gains go away when using hard attention based training. On the other hand, variational attention retains most of the performance gain but with training speed comparable to neural attention.

Computational workloads composing traditional Transformer models are starkly bifurcated. Multi-Head Attention (MHA) is memory-bound, with low arithmetic intensity, while feedforward layers are compute-bound. This dichotomy has long motivated research into specialized hardware to mitigate the MHA bottleneck. This paper argues that recent architectural shifts, namely Multi-head Latent Attention (MLA) and Mixture-of-Experts (MoE), challenge the premise of specialized attention hardware. We make two key observations. First, the arithmetic intensity of MLA is over two orders of magnitude greater than that of MHA, shifting it close to a compute-bound regime well-suited for modern accelerators like GPUs. Second, by distributing MoE experts across a pool of accelerators, their arithmetic intensity can be tuned through batching to match that of the dense layers, creating a more balanced computational profile. These findings reveal a diminishing need for specialized attention hardware. The central challenge for next-generation Transformers is no longer accelerating a single memory-bound layer. Instead, the focus must shift to designing balanced systems with sufficient compute, memory capacity, memory bandwidth, and high-bandwidth interconnects to manage the diverse demands of large-scale models.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

Proteins are complex biomolecules that perform a variety of crucial functions within living organisms. Designing and generating novel proteins can pave the way for many future synthetic biology applications, including drug discovery. However, it remains a challenging computational task due to the large modeling space of protein structures. In this study, we propose a latent diffusion model that can reduce the complexity of protein modeling while flexibly capturing the distribution of natural protein structures in a condensed latent space. Specifically, we propose an equivariant protein autoencoder that embeds proteins into a latent space and then uses an equivariant diffusion model to learn the distribution of the latent protein representations. Experimental results demonstrate that our method can effectively generate novel protein backbone structures with high designability and efficiency.

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This stands in contrast to mainstream reasoning models that scale up compute by producing more tokens. Unlike approaches based on chain-of-thought, our approach does not require any specialized training data, can work with small context windows, and can capture types of reasoning that are not easily represented in words. We scale a proof-of-concept model to 3.5 billion parameters and 800 billion tokens. We show that the resulting model can improve its performance on reasoning benchmarks, sometimes dramatically, up to a computation load equivalent to 50 billion parameters.

Generative models have enabled the creation of contents that are indistinguishable from those taken from nature. Open-source development of such models raised concerns about the risks of their misuse for malicious purposes. One potential risk mitigation strategy is to attribute generative models via fingerprinting. Current fingerprinting methods exhibit a significant tradeoff between robust attribution accuracy and generation quality while lacking design principles to improve this tradeoff. This paper investigates the use of latent semantic dimensions as fingerprints, from where we can analyze the effects of design variables, including the choice of fingerprinting dimensions, strength, and capacity, on the accuracy-quality tradeoff. Compared with previous SOTA, our method requires minimum computation and is more applicable to large-scale models. We use StyleGAN2 and the latent diffusion model to demonstrate the efficacy of our method.

Consistency models have demonstrated powerful capability in efficient image generation and allowed synthesis within a few sampling steps, alleviating the high computational cost in diffusion models. However, the consistency model in the more challenging and resource-consuming video generation is still less explored. In this report, we present the VideoLCM framework to fill this gap, which leverages the concept of consistency models from image generation to efficiently synthesize videos with minimal steps while maintaining high quality. VideoLCM builds upon existing latent video diffusion models and incorporates consistency distillation techniques for training the latent consistency model. Experimental results reveal the effectiveness of our VideoLCM in terms of computational efficiency, fidelity and temporal consistency. Notably, VideoLCM achieves high-fidelity and smooth video synthesis with only four sampling steps, showcasing the potential for real-time synthesis. We hope that VideoLCM can serve as a simple yet effective baseline for subsequent research. The source code and models will be publicly available.

By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a guiding mechanism to control the image generation process without retraining. However, since these models typically operate directly in pixel space, optimization of powerful DMs often consumes hundreds of GPU days and inference is expensive due to sequential evaluations. To enable DM training on limited computational resources while retaining their quality and flexibility, we apply them in the latent space of powerful pretrained autoencoders. In contrast to previous work, training diffusion models on such a representation allows for the first time to reach a near-optimal point between complexity reduction and detail preservation, greatly boosting visual fidelity. By introducing cross-attention layers into the model architecture, we turn diffusion models into powerful and flexible generators for general conditioning inputs such as text or bounding boxes and high-resolution synthesis becomes possible in a convolutional manner. Our latent diffusion models (LDMs) achieve a new state of the art for image inpainting and highly competitive performance on various tasks, including unconditional image generation, semantic scene synthesis, and super-resolution, while significantly reducing computational requirements compared to pixel-based DMs. Code is available at https://github.com/CompVis/latent-diffusion .

Video Variational Autoencoder (VAE) encodes videos into a low-dimensional latent space, becoming a key component of most Latent Video Diffusion Models (LVDMs) to reduce model training costs. However, as the resolution and duration of generated videos increase, the encoding cost of Video VAEs becomes a limiting bottleneck in training LVDMs. Moreover, the block-wise inference method adopted by most LVDMs can lead to discontinuities of latent space when processing long-duration videos. The key to addressing the computational bottleneck lies in decomposing videos into distinct components and efficiently encoding the critical information. Wavelet transform can decompose videos into multiple frequency-domain components and improve the efficiency significantly, we thus propose Wavelet Flow VAE (WF-VAE), an autoencoder that leverages multi-level wavelet transform to facilitate low-frequency energy flow into latent representation. Furthermore, we introduce a method called Causal Cache, which maintains the integrity of latent space during block-wise inference. Compared to state-of-the-art video VAEs, WF-VAE demonstrates superior performance in both PSNR and LPIPS metrics, achieving 2x higher throughput and 4x lower memory consumption while maintaining competitive reconstruction quality. Our code and models are available at https://github.com/PKU-YuanGroup/WF-VAE.

Generating long-form 44.1kHz stereo audio from text prompts can be computationally demanding. Further, most previous works do not tackle that music and sound effects naturally vary in their duration. Our research focuses on the efficient generation of long-form, variable-length stereo music and sounds at 44.1kHz using text prompts with a generative model. Stable Audio is based on latent diffusion, with its latent defined by a fully-convolutional variational autoencoder. It is conditioned on text prompts as well as timing embeddings, allowing for fine control over both the content and length of the generated music and sounds. Stable Audio is capable of rendering stereo signals of up to 95 sec at 44.1kHz in 8 sec on an A100 GPU. Despite its compute efficiency and fast inference, it is one of the best in two public text-to-music and -audio benchmarks and, differently from state-of-the-art models, can generate music with structure and stereo sounds.

Large language models (LLMs) demonstrate strong reasoning abilities with chain-of-thought prompting, but explicit reasoning introduces substantial computational overhead. Recent work on latent reasoning reduces this cost by reasoning in latent space without explicit supervision, but performance drops significantly. Our preliminary experiments suggest that this degradation stems from the unstructured latent space, which makes fitting latent tokens difficult. To address this, we restrict the latent space to the column space of the LLM vocabulary, treating latent reasoning as a superposition over vocabulary probabilities. Once latent reasoning concludes, it collapses into an eigenstate of explicit reasoning to yield the final answer. Based on this idea, we propose Latent-SFT, a two-stage learning framework. In the first stage, we design two specialized attention masks to guide the Latent Token Encoder in generating latent tokens, allowing the LLM to produce the correct answer conditioned on them. In the second stage, the Latent Token Encoder is discarded, and the LLM is directly trained to generate these latent tokens autonomously for latent reasoning, optimized with KL and CE losses. Latent-SFT sets a new state of the art on GSM8k, matching explicit SFT performance while cutting reasoning chains by up to 4 times and outperforming prior latent methods. On Math500 and AIME24, lexical probability-based latent reasoning also clearly surpasses hidden-state-based approaches. Our metrics of effective compression rate and effective global parallelism further show that latent reasoning is both the compression of a single path and the superposition of multiple paths.

Latent heat thermal energy storage (LHTES) systems are compelling candidates for energy storage, primarily owing to their high storage density. Improving their performance is crucial for developing the next-generation efficient and cost effective devices. Topology optimization (TO) has emerged as a powerful computational tool to design LHTES systems by optimally distributing a high-conductivity material (HCM) and a phase change material (PCM). However, conventional TO typically limits to optimizing the geometry for a fixed, pre-selected materials. This approach does not leverage the large and expanding databases of novel materials. Consequently, the co-design of material and geometry for LHTES remains a challenge and unexplored. To address this limitation, we present an automated design framework for the concurrent optimization of material choice and topology. A key challenge is the discrete nature of material selection, which is incompatible with the gradient-based methods used for TO. We overcome this by using a data-driven variational autoencoder (VAE) to project discrete material databases for both the HCM and PCM onto continuous and differentiable latent spaces. These continuous material representations are integrated into an end-to-end differentiable, transient nonlinear finite-element solver that accounts for phase change. We demonstrate this framework on a problem aimed at maximizing the discharged energy within a specified time, subject to cost constraints. The effectiveness of the proposed method is validated through several illustrative examples.

We present a comprehensive theoretical and empirical study of the Muon optimizer for training transformers only with a small to medium decoder (30M - 200M parameters), with an emphasis on its mathematical foundations, convergence properties and synergistic interactions with modern architectural optimizations. Building on recent work showing Muon's scalability, we provide rigorous theoretical analysis including: (i)showing the convergence rate under standard assumptions, (ii) spectral regularization properties that prevent gradient explosion, (iii) connection to natural gradient descent on the Stiefel manifold, and (iv) equivalence to steepest gradient descent under the spectral norm. Crucially, we demonstrate that Muon expands the Pareto frontier in the compute-time trade-off by maintaining superior data efficiency at large batch sizes, a key finding of~essentialai2025muon that we validate across our model scales. Empirically, Muon reaches the target loss with 48-52\% of the training calculated by AdamW while maintaining or improving the final perplexity, consistent with larger-scale results. When combined with Multi-Head Latent Attention (MLA) and Mixture-of-Experts (MoE), we observe multiplicative efficiency gains: MLA+MoE+Muon achieves 68\% memory reduction and 3.2times inference speedup, while improving perplexity by 8-12\%. We provide detailed procedures on 15 architectural and optimizer components, stability analyzes across 100+ training runs, and practical implementation guidelines including Newton-Schulz coefficients (3.4445, -4.7750, 2.0315) optimized by~su2024muonblog. Our theoretical analysis and comprehensive experiments establish Muon as a principled, robust alternative to AdamW that particularly excels when combined with modern efficiency techniques and large-batch training regimes.

Probabilistic decoding in Large Language Models (LLMs) often yields inconsistent outputs, particularly on complex or long-form questions. Self-Consistency (SC) mitigates this for short-form QA by majority voting over exact strings, whereas Universal Self-Consistency (USC) and Weighted Unigram Consistency Score (WUCS) extend to long-form responses but lose accuracy on short-form benchmarks. We introduce Latent Self-Consistency (LSC), which selects the most semantically consistent response using learnable token embeddings. LSC's lightweight forward processing of summary tokens only introduces negligible runtime overhead (at most 0.9%) on top of standard decoding of the base LLM, and requires no changes to the model architecture. Across 6 short-form and 5 long-form reasoning benchmarks (e.g., MATH, MMLU, TruthfulQA), LSC surpasses SC, USC, and WUCS on both short-form and long-form on average performance, while adding negligible computational overhead on vanilla inference. These results position LSC as a reliable consistency-selection method that works effectively across various answer formats. Additionally, LSC provides well-calibrated confidence estimates, maintaining low expected calibration error across both answer formats.

Latent Diffusion Models (LDMs) have emerged as powerful generative models, known for delivering remarkable results under constrained computational resources. However, deploying LDMs on resource-limited devices remains a complex issue, presenting challenges such as memory consumption and inference speed. To address this issue, we introduce LD-Pruner, a novel performance-preserving structured pruning method for compressing LDMs. Traditional pruning methods for deep neural networks are not tailored to the unique characteristics of LDMs, such as the high computational cost of training and the absence of a fast, straightforward and task-agnostic method for evaluating model performance. Our method tackles these challenges by leveraging the latent space during the pruning process, enabling us to effectively quantify the impact of pruning on model performance, independently of the task at hand. This targeted pruning of components with minimal impact on the output allows for faster convergence during training, as the model has less information to re-learn, thereby addressing the high computational cost of training. Consequently, our approach achieves a compressed model that offers improved inference speed and reduced parameter count, while maintaining minimal performance degradation. We demonstrate the effectiveness of our approach on three different tasks: text-to-image (T2I) generation, Unconditional Image Generation (UIG) and Unconditional Audio Generation (UAG). Notably, we reduce the inference time of Stable Diffusion (SD) by 34.9% while simultaneously improving its FID by 5.2% on MS-COCO T2I benchmark. This work paves the way for more efficient pruning methods for LDMs, enhancing their applicability.

Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Proper Orthogonal Decomposition (POD) coefficient space, exploiting the orthogonality of POD modes to impose an interpretable, variance-ordered latent geometry. This design enables efficient ensemble generation, preserves dominant spatial structure, and yields spatially interpretable, well-calibrated uncertainty at substantially lower computational cost. We evaluate PODiff on sea surface temperature downscaling over the West Australian coast and on a controlled advection-diffusion benchmark. PODiff achieves reconstruction accuracy comparable to pixel-space diffusion while requiring significantly less memory and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.

Chest X-Ray (CXR) imaging for pulmonary diagnosis raises significant challenges, primarily because bone structures can obscure critical details necessary for accurate diagnosis. Recent advances in deep learning, particularly with diffusion models, offer significant promise for effectively minimizing the visibility of bone structures in CXR images, thereby improving clarity and diagnostic accuracy. Nevertheless, existing diffusion-based methods for bone suppression in CXR imaging struggle to balance the complete suppression of bones with preserving local texture details. Additionally, their high computational demand and extended processing time hinder their practical use in clinical settings. To address these limitations, we introduce a Global-Local Latent Consistency Model (GL-LCM) architecture. This model combines lung segmentation, dual-path sampling, and global-local fusion, enabling fast high-resolution bone suppression in CXR images. To tackle potential boundary artifacts and detail blurring in local-path sampling, we further propose Local-Enhanced Guidance, which addresses these issues without additional training. Comprehensive experiments on a self-collected dataset SZCH-X-Rays, and the public dataset JSRT, reveal that our GL-LCM delivers superior bone suppression and remarkable computational efficiency, significantly outperforming several competitive methods. Our code is available at https://github.com/diaoquesang/GL-LCM.

LLM self-evaluation relies on the LLM's own ability to estimate response correctness, which can greatly improve its deployment reliability. In this research track, we propose the Chain-of-Embedding (CoE) in the latent space to enable LLMs to perform output-free self-evaluation. CoE consists of all progressive hidden states produced during the inference time, which can be treated as the latent thinking path of LLMs. We find that when LLMs respond correctly and incorrectly, their CoE features differ, these discrepancies assist us in estimating LLM response correctness. Experiments in four diverse domains and seven LLMs fully demonstrate the effectiveness of our method. Meanwhile, its label-free design intent without any training and millisecond-level computational cost ensures real-time feedback in large-scale scenarios. More importantly, we provide interesting insights into LLM response correctness from the perspective of hidden state changes inside LLMs.

Memory retention challenges in deep neural architectures have ongoing limitations in the ability to process and recall extended contextual information. Token dependencies degrade as sequence length increases, leading to a decline in coherence and factual consistency across longer outputs. A structured approach is introduced to mitigate this issue through the reweaving of latent states captured at different processing layers, reinforcing token representations over extended sequences. The proposed Contextual Memory Reweaving framework incorporates a Layered Latent State Reconstruction mechanism to systematically integrate past contextual embeddings without introducing external memory modules. Experimental results demonstrate improvements in recall accuracy across a range of sequence lengths, with notable gains in the retention of rarely occurring tokens and numerical reasoning consistency. Further analysis of computational efficiency indicates that the additional processing overhead remains within acceptable thresholds, enabling scalability across different model sizes. Evaluations in long-form text generation and ambiguous query resolution highlight the capacity of memory reweaving to enhance continuity and reduce inconsistencies over extended outputs. Attention weight distributions reveal more structured allocation patterns, suggesting that reweaved latent states contribute to improved contextual awareness. The findings establish a framework for refining memory retention mechanisms in language models, addressing long-standing challenges in handling complex, multi-step reasoning tasks.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

Text-guided image generation has progressed rapidly in recent years, inspiring major breakthroughs in text-guided shape generation. Recently, it has been shown that using score distillation, one can successfully text-guide a NeRF model to generate a 3D object. We adapt the score distillation to the publicly available, and computationally efficient, Latent Diffusion Models, which apply the entire diffusion process in a compact latent space of a pretrained autoencoder. As NeRFs operate in image space, a naive solution for guiding them with latent score distillation would require encoding to the latent space at each guidance step. Instead, we propose to bring the NeRF to the latent space, resulting in a Latent-NeRF. Analyzing our Latent-NeRF, we show that while Text-to-3D models can generate impressive results, they are inherently unconstrained and may lack the ability to guide or enforce a specific 3D structure. To assist and direct the 3D generation, we propose to guide our Latent-NeRF using a Sketch-Shape: an abstract geometry that defines the coarse structure of the desired object. Then, we present means to integrate such a constraint directly into a Latent-NeRF. This unique combination of text and shape guidance allows for increased control over the generation process. We also show that latent score distillation can be successfully applied directly on 3D meshes. This allows for generating high-quality textures on a given geometry. Our experiments validate the power of our different forms of guidance and the efficiency of using latent rendering. Implementation is available at https://github.com/eladrich/latent-nerf

While explicit Chain-of-Thought (CoT) equips Large Language Models (LLMs) with strong reasoning capabilities, it requires models to verbalize every intermediate step in text tokens, constraining the model thoughts to the discrete vocabulary space. Recently, reasoning in continuous latent space has emerged as a promising alternative, enabling more robust inference and flexible computation beyond discrete token constraints. However, current latent paradigms often suffer from feature collapse and instability, stemming from distribution mismatches when recurrently using hidden states as the input embeddings, or alignment issues when relying on assistant models. To address this, we propose Latent Thoughts Tuning (LT-Tuning), a framework that redefines how latent thoughts are constructed and deployed. Instead of relying solely on raw hidden states, our method introduces a Context-Prediction-Fusion mechanism that jointly leveraging contextual hidden states and predictive semantic guidance from the vocabulary embedding space. Combined with a progressive three-stage curriculum learning pipeline, LT-Tuning also enables dynamically switching between latent and explicit thinking modes. Experiments demonstrate that our method outperforms existing latent reasoning baselines, effectively mitigating feature collapse and achieving robust reasoning accuracy.

Current genomic foundation models (GFMs) rely on extensive neural computation to implicitly approximate conserved biological motifs from single-nucleotide inputs. We propose Gengram, a conditional memory module that introduces an explicit and highly efficient lookup primitive for multi-base motifs via a genomic-specific hashing scheme, establishing genomic "syntax". Integrated into the backbone of state-of-the-art GFMs, Gengram achieves substantial gains (up to 14%) across several functional genomics tasks. The module demonstrates robust architectural generalization, while further inspection of Gengram's latent space reveals the emergence of meaningful representations that align closely with fundamental biological knowledge. By establishing structured motif memory as a modeling primitive, Gengram simultaneously boosts empirical performance and mechanistic interpretability, providing a scalable and biology-aligned pathway for the next generation of GFMs. The code is available at https://github.com/zhejianglab/Genos, and the model checkpoint is available at https://huggingface.co/ZhejiangLab/Gengram.

We present an approach to tackle the speaker recognition problem using Triplet Neural Networks. Currently, the i-vector representation with probabilistic linear discriminant analysis (PLDA) is the most commonly used technique to solve this problem, due to high classification accuracy with a relatively short computation time. In this paper, we explore a neural network approach, namely Triplet Neural Networks (TNNs), to built a latent space for different classifiers to solve the Multi-Target Speaker Detection and Identification Challenge Evaluation 2018 (MCE 2018) dataset. This training set contains i-vectors from 3,631 speakers, with only 3 samples for each speaker, thus making speaker recognition a challenging task. When using the train and development set for training both the TNN and baseline model (i.e., similarity evaluation directly on the i-vector representation), our proposed model outperforms the baseline by 23%. When reducing the training data to only using the train set, our method results in 309 confusions for the Multi-target speaker identification task, which is 46% better than the baseline model. These results show that the representational power of TNNs is especially evident when training on small datasets with few instances available per class.

Preference optimization for diffusion and flow-matching models relies on reward functions that are both discriminatively robust and computationally efficient. Vision-Language Models (VLMs) have emerged as the primary reward provider, leveraging their rich multimodal priors to guide alignment. However, their computation and memory cost can be substantial, and optimizing a latent diffusion generator through a pixel-space reward introduces a domain mismatch that complicates alignment. In this paper, we propose DiNa-LRM, a diffusion-native latent reward model that formulates preference learning directly on noisy diffusion states. Our method introduces a noise-calibrated Thurstone likelihood with diffusion-noise-dependent uncertainty. DiNa-LRM leverages a pretrained latent diffusion backbone with a timestep-conditioned reward head, and supports inference-time noise ensembling, providing a diffusion-native mechanism for test-time scaling and robust rewarding. Across image alignment benchmarks, DiNa-LRM substantially outperforms existing diffusion-based reward baselines and achieves performance competitive with state-of-the-art VLMs at a fraction of the computational cost. In preference optimization, we demonstrate that DiNa-LRM improves preference optimization dynamics, enabling faster and more resource-efficient model alignment.

Sequential recommender systems have become increasingly important in real-world applications that model user behavior sequences to predict their preferences. However, existing sequential recommendation methods predominantly rely on non-reasoning paradigms, which may limit the model's computational capacity and result in suboptimal recommendation performance. To address these limitations, we present LARES, a novel and scalable LAtent REasoning framework for Sequential recommendation that enhances model's representation capabilities through increasing the computation density of parameters by depth-recurrent latent reasoning. Our proposed approach employs a recurrent architecture that allows flexible expansion of reasoning depth without increasing parameter complexity, thereby effectively capturing dynamic and intricate user interest patterns. A key difference of LARES lies in refining all input tokens at each implicit reasoning step to improve the computation utilization. To fully unlock the model's reasoning potential, we design a two-phase training strategy: (1) Self-supervised pre-training (SPT) with dual alignment objectives; (2) Reinforcement post-training (RPT). During the first phase, we introduce trajectory-level alignment and step-level alignment objectives, which enable the model to learn recommendation-oriented latent reasoning patterns without requiring supplementary annotated data. The subsequent phase utilizes reinforcement learning (RL) to harness the model's exploratory ability, further refining its reasoning capabilities. Comprehensive experiments on real-world benchmarks demonstrate our framework's superior performance. Notably, LARES exhibits seamless compatibility with existing advanced models, further improving their recommendation performance. Our code is available at https://anonymous.4open.science/r/LARES-E458/.

Imagining the future trajectory is the key for robots to make sound planning and successfully reach their goals. Therefore, text-conditioned video prediction (TVP) is an essential task to facilitate general robot policy learning. To tackle this task and empower robots with the ability to foresee the future, we propose a sample and computation-efficient model, named Seer, by inflating the pretrained text-to-image (T2I) stable diffusion models along the temporal axis. We enhance the U-Net and language conditioning model by incorporating computation-efficient spatial-temporal attention. Furthermore, we introduce a novel Frame Sequential Text Decomposer module that dissects a sentence's global instruction into temporally aligned sub-instructions, ensuring precise integration into each frame of generation. Our framework allows us to effectively leverage the extensive prior knowledge embedded in pretrained T2I models across the frames. With the adaptable-designed architecture, Seer makes it possible to generate high-fidelity, coherent, and instruction-aligned video frames by fine-tuning a few layers on a small amount of data. The experimental results on Something Something V2 (SSv2), Bridgedata and EpicKitchens-100 datasets demonstrate our superior video prediction performance with around 480-GPU hours versus CogVideo with over 12,480-GPU hours: achieving the 31% FVD improvement compared to the current SOTA model on SSv2 and 83.7% average preference in the human evaluation.

Multi-agent systems (MAS) extend large language models (LLMs) from independent single-model reasoning to coordinative system-level intelligence. While existing LLM agents depend on text-based mediation for reasoning and communication, we take a step forward by enabling models to collaborate directly within the continuous latent space. We introduce LatentMAS, an end-to-end training-free framework that enables pure latent collaboration among LLM agents. In LatentMAS, each agent first performs auto-regressive latent thoughts generation through last-layer hidden embeddings. A shared latent working memory then preserves and transfers each agent's internal representations, ensuring lossless information exchange. We provide theoretical analyses establishing that LatentMAS attains higher expressiveness and lossless information preservation with substantially lower complexity than vanilla text-based MAS. In addition, empirical evaluations across 9 comprehensive benchmarks spanning math and science reasoning, commonsense understanding, and code generation show that LatentMAS consistently outperforms strong single-model and text-based MAS baselines, achieving up to 14.6% higher accuracy, reducing output token usage by 70.8%-83.7%, and providing 4x-4.3x faster end-to-end inference. These results demonstrate that our new latent collaboration framework enhances system-level reasoning quality while offering substantial efficiency gains without any additional training. Code and data are fully open-sourced at https://github.com/Gen-Verse/LatentMAS.

We introduce the Byte Latent Transformer (BLT), a new byte-level LLM architecture that, for the first time, matches tokenization-based LLM performance at scale with significant improvements in inference efficiency and robustness. BLT encodes bytes into dynamically sized patches, which serve as the primary units of computation. Patches are segmented based on the entropy of the next byte, allocating more compute and model capacity where increased data complexity demands it. We present the first FLOP controlled scaling study of byte-level models up to 8B parameters and 4T training bytes. Our results demonstrate the feasibility of scaling models trained on raw bytes without a fixed vocabulary. Both training and inference efficiency improve due to dynamically selecting long patches when data is predictable, along with qualitative improvements on reasoning and long tail generalization. Overall, for fixed inference costs, BLT shows significantly better scaling than tokenization-based models, by simultaneously growing both patch and model size.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, especially when guided by explicit chain-of-thought (CoT) reasoning that verbalizes intermediate steps. While CoT improves both interpretability and accuracy, its dependence on natural language reasoning limits the model's expressive bandwidth. Latent reasoning tackles this bottleneck by performing multi-step inference entirely in the model's continuous hidden state, eliminating token-level supervision. To advance latent reasoning research, this survey provides a comprehensive overview of the emerging field of latent reasoning. We begin by examining the foundational role of neural network layers as the computational substrate for reasoning, highlighting how hierarchical representations support complex transformations. Next, we explore diverse latent reasoning methodologies, including activation-based recurrence, hidden state propagation, and fine-tuning strategies that compress or internalize explicit reasoning traces. Finally, we discuss advanced paradigms such as infinite-depth latent reasoning via masked diffusion models, which enable globally consistent and reversible reasoning processes. By unifying these perspectives, we aim to clarify the conceptual landscape of latent reasoning and chart future directions for research at the frontier of LLM cognition. An associated GitHub repository collecting the latest papers and repos is available at: https://github.com/multimodal-art-projection/LatentCoT-Horizon/.

While Chain-of-Thought (CoT) significantly enhances the performance of Large Language Models (LLMs), explicit reasoning chains introduce substantial computational redundancy. Recent latent reasoning methods attempt to mitigate this by compressing reasoning processes into latent space, but often suffer from severe performance degradation due to the lack of appropriate compression guidance. In this study, we propose Rendered CoT-Guided variational Latent Reasoning (ReGuLaR), a simple yet novel latent learning paradigm resolving this issue. Fundamentally, we formulate latent reasoning within the Variational Auto-Encoding (VAE) framework, sampling the current latent reasoning state from the posterior distribution conditioned on previous ones. Specifically, when learning this variational latent reasoning model, we render explicit reasoning chains as images, from which we extract dense visual-semantic representations to regularize the posterior distribution, thereby achieving efficient compression with minimal information loss. Extensive experiments demonstrate that ReGuLaR significantly outperforms existing latent reasoning methods across both computational efficiency and reasoning effectiveness, and even surpasses CoT through multi-modal reasoning, providing a new and insightful solution to latent reasoning. Code: https://github.com/FanmengWang/ReGuLaR.

"Thinking with images" has emerged as an effective paradigm for advancing visual reasoning, extending beyond text-only chains of thought by injecting visual evidence into intermediate reasoning steps. However, existing methods fall short of human-like abstract visual thinking, as their flexibility is fundamentally limited by external tools. In this work, we introduce Monet, a training framework that enables multimodal large language models (MLLMs) to reason directly within the latent visual space by generating continuous embeddings that function as intermediate visual thoughts. We identify two core challenges in training MLLMs for latent visual reasoning: high computational cost in latent-vision alignment and insufficient supervision over latent embeddings, and address them with a three-stage distillation-based supervised fine-tuning (SFT) pipeline. We further reveal a limitation of applying GRPO to latent reasoning: it primarily enhances text-based reasoning rather than latent reasoning. To overcome this, we propose VLPO (Visual-latent Policy Optimization), a reinforcement learning method that explicitly incorporates latent embeddings into policy gradient updates. To support SFT, we construct Monet-SFT-125K, a high-quality text-image interleaved CoT dataset containing 125K real-world, chart, OCR, and geometry CoTs. Our model, Monet-7B, shows consistent gains across real-world perception and reasoning benchmarks and exhibits strong out-of-distribution generalization on challenging abstract visual reasoning tasks. We also empirically analyze the role of each training component and discuss our early unsuccessful attempts, providing insights for future developments in visual latent reasoning. Our model, data, and code are available at https://github.com/NOVAglow646/Monet.

Recent progress in generative models has significantly improved image restoration capabilities, particularly through powerful diffusion models that offer remarkable recovery of semantic details and local fidelity. However, deploying these models at ultra-high resolutions faces a critical trade-off between quality and efficiency due to the computational demands of long-range attention mechanisms. To address this, we introduce ZipIR, a novel framework that enhances efficiency, scalability, and long-range modeling for high-res image restoration. ZipIR employs a highly compressed latent representation that compresses image 32x, effectively reducing the number of spatial tokens, and enabling the use of high-capacity models like the Diffusion Transformer (DiT). Toward this goal, we propose a Latent Pyramid VAE (LP-VAE) design that structures the latent space into sub-bands to ease diffusion training. Trained on full images up to 2K resolution, ZipIR surpasses existing diffusion-based methods, offering unmatched speed and quality in restoring high-resolution images from severely degraded inputs.

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped architectures possess an inductive bias toward latent reasoning. However, prior approaches fix the number of loop iterations during training and inference, leaving open the question of whether these models can flexibly adapt their computational depth under variable compute budgets. We introduce LoopFormer, a looped Transformer trained on variable-length trajectories to enable budget-conditioned reasoning. Our core contribution is a shortcut-consistency training scheme that aligns trajectories of different lengths, ensuring that shorter loops yield informative representations while longer loops continue to refine them. LoopFormer conditions each loop on the current time and step size, enabling representations to evolve consistently across trajectories of varying length rather than drifting or stagnating. Empirically, LoopFormer demonstrates robust performance on language modeling and reasoning benchmarks even under aggressive compute constraints, while scaling gracefully with additional budget. These results show that looped Transformers are inherently suited for adaptive language modeling, opening a path toward controllable and budget-aware large language models.

Learning from human feedback typically relies on preference optimization that constrains policy updates through token-level regularization. However, preference optimization for language models is particularly challenging because token-space similarity does not imply semantic or behavioral similarity. To address this challenge, we leverage latent-space regularization for language model preference optimization. We introduce GANPO, which achieves latent-space regularization by penalizing divergence between the internal representations of a policy model and a reference model. Given that latent representations are not associated with explicit probability densities, we adopt an adversarial approach inspired by GANs to minimize latent-space divergence. We integrate GANPO as a regularizer into existing offline preference optimization objectives. Experiments across multiple model architectures and tasks show consistent improvements from latent-space regularization. Further, by comparing GANPO-induced inferential biases with those from token-level regularization, we find that GANPO provides more robust structural feedback under distributional shift and noise while maintaining comparable downstream performance with minor computational overhead.

Chain-of-Thought (CoT) empowers Large Language Models (LLMs) to tackle complex problems, but remains constrained by the computational cost and reasoning path collapse when grounded in discrete token spaces. Recent latent reasoning approaches attempt to optimize efficiency by performing reasoning within continuous hidden states. However, these methods typically operate as opaque end-to-end mappings from explicit reasoning steps to latent states, and often require a pre-defined number of latent steps during inference. In this work, we introduce PLaT (Planning with Latent Thoughts), a framework that reformulates latent reasoning as planning by fundamentally decouple reasoning from verbalization. We model reasoning as a deterministic trajectory of latent planning states, while a separate Decoder grounds these thoughts into text when necessary. This decoupling allows the model to dynamically determine when to terminate reasoning rather than relying on fixed hyperparameters. Empirical results on mathematical benchmarks reveal a distinct trade-off: while PLaT achieves lower greedy accuracy than baselines, it demonstrates superior scalability in terms of reasoning diversity. This indicates that PLaT learns a robust, broader solution space, offering a transparent and scalable foundation for inference-time search.

This study presents Latent Diffusion Autoencoder (LDAE), a novel encoder-decoder diffusion-based framework for efficient and meaningful unsupervised learning in medical imaging, focusing on Alzheimer disease (AD) using brain MR from the ADNI database as a case study. Unlike conventional diffusion autoencoders operating in image space, LDAE applies the diffusion process in a compressed latent representation, improving computational efficiency and making 3D medical imaging representation learning tractable. To validate the proposed approach, we explore two key hypotheses: (i) LDAE effectively captures meaningful semantic representations on 3D brain MR associated with AD and ageing, and (ii) LDAE achieves high-quality image generation and reconstruction while being computationally efficient. Experimental results support both hypotheses: (i) linear-probe evaluations demonstrate promising diagnostic performance for AD (ROC-AUC: 90%, ACC: 84%) and age prediction (MAE: 4.1 years, RMSE: 5.2 years); (ii) the learned semantic representations enable attribute manipulation, yielding anatomically plausible modifications; (iii) semantic interpolation experiments show strong reconstruction of missing scans, with SSIM of 0.969 (MSE: 0.0019) for a 6-month gap. Even for longer gaps (24 months), the model maintains robust performance (SSIM > 0.93, MSE < 0.004), indicating an ability to capture temporal progression trends; (iv) compared to conventional diffusion autoencoders, LDAE significantly increases inference throughput (20x faster) while also enhancing reconstruction quality. These findings position LDAE as a promising framework for scalable medical imaging applications, with the potential to serve as a foundation model for medical image analysis. Code available at https://github.com/GabrieleLozupone/LDAE

Recently, there has been tremendous progress in visual synthesis and the underlying generative models. Here, diffusion models (DMs) stand out particularly, but lately, flow matching (FM) has also garnered considerable interest. While DMs excel in providing diverse images, they suffer from long training and slow generation. With latent diffusion, these issues are only partially alleviated. Conversely, FM offers faster training and inference but exhibits less diversity in synthesis. We demonstrate that introducing FM between the Diffusion model and the convolutional decoder offers high-resolution image synthesis with reduced computational cost and model size. Diffusion can then efficiently provide the necessary generation diversity. FM compensates for the lower resolution, mapping the small latent space to a high-dimensional one. Subsequently, the convolutional decoder of the LDM maps these latents to high-resolution images. By combining the diversity of DMs, the efficiency of FMs, and the effectiveness of convolutional decoders, we achieve state-of-the-art high-resolution image synthesis at 1024^2 with minimal computational cost. Importantly, our approach is orthogonal to recent approximation and speed-up strategies for the underlying DMs, making it easily integrable into various DM frameworks.

We present LatentCSI, a novel method for generating images of the physical environment from WiFi CSI measurements that leverages a pretrained latent diffusion model (LDM). Unlike prior approaches that rely on complex and computationally intensive techniques such as GANs, our method employs a lightweight neural network to map CSI amplitudes directly into the latent space of an LDM. We then apply the LDM's denoising diffusion model to the latent representation with text-based guidance before decoding using the LDM's pretrained decoder to obtain a high-resolution image. This design bypasses the challenges of pixel-space image generation and avoids the explicit image encoding stage typically required in conventional image-to-image pipelines, enabling efficient and high-quality image synthesis. We validate our approach on two datasets: a wide-band CSI dataset we collected with off-the-shelf WiFi devices and cameras; and a subset of the publicly available MM-Fi dataset. The results demonstrate that LatentCSI outperforms baselines of comparable complexity trained directly on ground-truth images in both computational efficiency and perceptual quality, while additionally providing practical advantages through its unique capacity for text-guided controllability.

Human motion synthesis conditioned on textual input has gained significant attention in recent years due to its potential applications in various domains such as gaming, film production, and virtual reality. Conditioned Motion synthesis takes a text input and outputs a 3D motion corresponding to the text. While previous works have explored motion synthesis using raw motion data and latent space representations with diffusion models, these approaches often suffer from high training and inference times. In this paper, we introduce a novel framework that utilizes Generative Adversarial Networks (GANs) in the latent space to enable faster training and inference while achieving results comparable to those of the state-of-the-art diffusion methods. We perform experiments on the HumanML3D, HumanAct12 benchmarks and demonstrate that a remarkably simple GAN in the latent space achieves a FID of 0.482 with more than 91% in FLOPs reduction compared to latent diffusion model. Our work opens up new possibilities for efficient and high-quality motion synthesis using latent space GANs.

Precise camera pose control is crucial for video generation with diffusion models. Existing methods require fine-tuning with additional datasets containing paired videos and camera pose annotations, which are both data-intensive and computationally costly, and can disrupt the pre-trained model distribution. We introduce Latent-Reframe, which enables camera control in a pre-trained video diffusion model without fine-tuning. Unlike existing methods, Latent-Reframe operates during the sampling stage, maintaining efficiency while preserving the original model distribution. Our approach reframes the latent code of video frames to align with the input camera trajectory through time-aware point clouds. Latent code inpainting and harmonization then refine the model latent space, ensuring high-quality video generation. Experimental results demonstrate that Latent-Reframe achieves comparable or superior camera control precision and video quality to training-based methods, without the need for fine-tuning on additional datasets.

Diffusion models have revolutionized image generation, yet several challenges restrict their application to large-image domains, such as digital pathology and satellite imagery. Given that it is infeasible to directly train a model on 'whole' images from domains with potential gigapixel sizes, diffusion-based generative methods have focused on synthesizing small, fixed-size patches extracted from these images. However, generating small patches has limited applicability since patch-based models fail to capture the global structures and wider context of large images, which can be crucial for synthesizing (semantically) accurate samples. To overcome this limitation, we present ZoomLDM, a diffusion model tailored for generating images across multiple scales. Central to our approach is a novel magnification-aware conditioning mechanism that utilizes self-supervised learning (SSL) embeddings and allows the diffusion model to synthesize images at different 'zoom' levels, i.e., fixed-size patches extracted from large images at varying scales. ZoomLDM synthesizes coherent histopathology images that remain contextually accurate and detailed at different zoom levels, achieving state-of-the-art image generation quality across all scales and excelling in the data-scarce setting of generating thumbnails of entire large images. The multi-scale nature of ZoomLDM unlocks additional capabilities in large image generation, enabling computationally tractable and globally coherent image synthesis up to 4096 times 4096 pixels and 4times super-resolution. Additionally, multi-scale features extracted from ZoomLDM are highly effective in multiple instance learning experiments.

Autoregressive models for text sometimes generate repetitive and low-quality output because errors accumulate during the steps of generation. This issue is often attributed to exposure bias - the difference between how a model is trained, and how it is used during inference. Denoising diffusion models provide an alternative approach in which a model can revisit and revise its output. However, they can be computationally expensive and prior efforts on text have led to models that produce less fluent output compared to autoregressive models, especially for longer text and paragraphs. In this paper, we propose PLANNER, a model that combines latent semantic diffusion with autoregressive generation, to generate fluent text while exercising global control over paragraphs. The model achieves this by combining an autoregressive "decoding" module with a "planning" module that uses latent diffusion to generate semantic paragraph embeddings in a coarse-to-fine manner. The proposed method is evaluated on various conditional generation tasks, and results on semantic generation, text completion and summarization show its effectiveness in generating high-quality long-form text in an efficient manner.

Conditional diffusion models rely on language-to-image alignment methods to steer the generation towards semantically accurate outputs. Despite the success of this architecture, misalignment and hallucinations remain common issues and require automatic misalignment detection tools to improve quality, for example by applying them in a Best-of-N (BoN) post-generation setting. Unfortunately, measuring the alignment after the generation is an expensive step since we need to wait for the overall generation to finish to determine prompt adherence. In contrast, this work hypothesizes that text/image misalignments can be detected early in the denoising process, enabling real-time alignment assessment without waiting for the complete generation. In particular, we propose NoisyCLIP a method that measures semantic alignment in the noisy latent space. This work is the first to explore and benchmark prompt-to-latent misalignment detection during image generation using dual encoders in the reverse diffusion process. We evaluate NoisyCLIP qualitatively and quantitatively and find it reduces computational cost by 50% while achieving 98% of CLIP alignment performance in BoN settings. This approach enables real-time alignment assessment during generation, reducing costs without sacrificing semantic fidelity.

Large language models (LLMs) demonstrate impressive capabilities in various language tasks but are susceptible to jailbreak attacks that circumvent their safety alignments. This paper introduces Latent Fusion Jailbreak (LFJ), a representation-based attack that interpolates hidden states from harmful and benign query pairs to elicit prohibited responses. LFJ begins by selecting query pairs with high thematic and syntactic similarity, then performs gradient-guided interpolation at influential layers and tokens, followed by optimization to balance attack success, output fluency, and computational efficiency. Evaluations on models such as Vicuna and LLaMA-2 across benchmarks like AdvBench and MaliciousInstruct yield an average attack success rate (ASR) of 94.01%, outperforming existing methods. To mitigate LFJ, we propose an adversarial training defense that fine-tunes models on interpolated examples, reducing ASR by over 80% without degrading performance on benign inputs. Ablation studies validate the importance of query pair selection, hidden state interpolation components, and optimization strategies in LFJ's effectiveness.

Deploying large language models (LLMs) often faces challenges from substantial memory and computational costs. Quantization offers a solution, yet performance degradation in the sub-1-bit regime remains particularly difficult. This paper introduces LittleBit, a novel method for extreme LLM compression. It targets levels like 0.1 bits per weight (BPW), achieving nearly 31times memory reduction, e.g., Llama2-13B to under 0.9 GB. LittleBit represents weights in a low-rank form using latent matrix factorization, subsequently binarizing these factors. To counteract information loss from this extreme precision, it integrates a multi-scale compensation mechanism. This includes row, column, and an additional latent dimension that learns per-rank importance. Two key contributions enable effective training: Dual Sign-Value-Independent Decomposition (Dual-SVID) for stable quantization-aware training (QAT) initialization, and integrated Residual Compensation to mitigate errors. Extensive experiments confirm LittleBit's superiority in sub-1-bit quantization: e.g., its 0.1 BPW performance on Llama2-7B surpasses the leading method's 0.7 BPW. This establishes a superior size-performance trade-off, with kernel-level benchmarks indicating potential for a 5times speedup compared to FP16. LittleBit paves the way for deploying powerful LLMs in resource-constrained environments.

Diffusion Transformer(DiT)-based generation models have achieved remarkable success in video generation. However, their inherent computational demands pose significant efficiency challenges. In this paper, we exploit the inherent temporal non-uniformity of real-world videos and observe that videos exhibit dynamic information density, with high-motion segments demanding greater detail preservation than static scenes. Inspired by this temporal non-uniformity, we propose VGDFR, a training-free approach for Diffusion-based Video Generation with Dynamic Latent Frame Rate. VGDFR adaptively adjusts the number of elements in latent space based on the motion frequency of the latent space content, using fewer tokens for low-frequency segments while preserving detail in high-frequency segments. Specifically, our key contributions are: (1) A dynamic frame rate scheduler for DiT video generation that adaptively assigns frame rates for video segments. (2) A novel latent-space frame merging method to align latent representations with their denoised counterparts before merging those redundant in low-resolution space. (3) A preference analysis of Rotary Positional Embeddings (RoPE) across DiT layers, informing a tailored RoPE strategy optimized for semantic and local information capture. Experiments show that VGDFR can achieve a speedup up to 3x for video generation with minimal quality degradation.

Instead of performing text-conditioned denoising in the image domain, latent diffusion models (LDMs) operate in latent space of a variational autoencoder (VAE), enabling more efficient processing at reduced computational costs. However, while the diffusion process has moved to the latent space, the contrastive language-image pre-training (CLIP) models, as used in many image processing tasks, still operate in pixel space. Doing so requires costly VAE-decoding of latent images before they can be processed. In this paper, we introduce Latent-CLIP, a CLIP model that operates directly in the latent space. We train Latent-CLIP on 2.7B pairs of latent images and descriptive texts, and show that it matches zero-shot classification performance of similarly sized CLIP models on both the ImageNet benchmark and a LDM-generated version of it, demonstrating its effectiveness in assessing both real and generated content. Furthermore, we construct Latent-CLIP rewards for reward-based noise optimization (ReNO) and show that they match the performance of their CLIP counterparts on GenEval and T2I-CompBench while cutting the cost of the total pipeline by 21%. Finally, we use Latent-CLIP to guide generation away from harmful content, achieving strong performance on the inappropriate image prompts (I2P) benchmark and a custom evaluation, without ever requiring the costly step of decoding intermediate images.

As Large Language Models (LLMs) are increasingly deployed in specialized domains with continuously evolving knowledge, the need for timely and precise knowledge injection has become essential. Fine-tuning with paraphrased data is a common approach to enhance knowledge injection, yet it faces two significant challenges: high computational costs due to repetitive external model usage and limited sample diversity. To this end, we introduce LaPael, a latent-level paraphrasing method that applies input-dependent noise to early LLM layers. This approach enables diverse and semantically consistent augmentations directly within the model. Furthermore, it eliminates the recurring costs of paraphrase generation for each knowledge update. Our extensive experiments on question-answering benchmarks demonstrate that LaPael improves knowledge injection over standard fine-tuning and existing noise-based approaches. Additionally, combining LaPael with data-level paraphrasing further enhances performance.

Diffusion models have recently shown the ability to generate high-quality images. However, controlling its generation process still poses challenges. The image style transfer task is one of those challenges that transfers the visual attributes of a style image to another content image. Typical obstacle of this task is the requirement of additional training of a pre-trained model. We propose a training-free style transfer algorithm, Style Tracking Reverse Diffusion Process (STRDP) for a pretrained Latent Diffusion Model (LDM). Our algorithm employs Adaptive Instance Normalization (AdaIN) function in a distinct manner during the reverse diffusion process of an LDM while tracking the encoding history of the style image. This algorithm enables style transfer in the latent space of LDM for reduced computational cost, and provides compatibility for various LDM models. Through a series of experiments and a user study, we show that our method can quickly transfer the style of an image without additional training. The speed, compatibility, and training-free aspect of our algorithm facilitates agile experiments with combinations of styles and LDMs for extensive application.

Sampling from the posterior distribution poses a major computational challenge in solving inverse problems using latent diffusion models. Common methods rely on Tweedie's first-order moments, which are known to induce a quality-limiting bias. Existing second-order approximations are impractical due to prohibitive computational costs, making standard reverse diffusion processes intractable for posterior sampling. This paper introduces Second-order Tweedie sampler from Surrogate Loss (STSL), a novel sampler that offers efficiency comparable to first-order Tweedie with a tractable reverse process using second-order approximation. Our theoretical results reveal that the second-order approximation is lower bounded by our surrogate loss that only requires O(1) compute using the trace of the Hessian, and by the lower bound we derive a new drift term to make the reverse process tractable. Our method surpasses SoTA solvers PSLD and P2L, achieving 4X and 8X reduction in neural function evaluations, respectively, while notably enhancing sampling quality on FFHQ, ImageNet, and COCO benchmarks. In addition, we show STSL extends to text-guided image editing and addresses residual distortions present from corrupted images in leading text-guided image editing methods. To our best knowledge, this is the first work to offer an efficient second-order approximation in solving inverse problems using latent diffusion and editing real-world images with corruptions.

We propose Latent-Shift -- an efficient text-to-video generation method based on a pretrained text-to-image generation model that consists of an autoencoder and a U-Net diffusion model. Learning a video diffusion model in the latent space is much more efficient than in the pixel space. The latter is often limited to first generating a low-resolution video followed by a sequence of frame interpolation and super-resolution models, which makes the entire pipeline very complex and computationally expensive. To extend a U-Net from image generation to video generation, prior work proposes to add additional modules like 1D temporal convolution and/or temporal attention layers. In contrast, we propose a parameter-free temporal shift module that can leverage the spatial U-Net as is for video generation. We achieve this by shifting two portions of the feature map channels forward and backward along the temporal dimension. The shifted features of the current frame thus receive the features from the previous and the subsequent frames, enabling motion learning without additional parameters. We show that Latent-Shift achieves comparable or better results while being significantly more efficient. Moreover, Latent-Shift can generate images despite being finetuned for T2V generation.