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Deep Learning · Generative Models and Autoencoders

Xuechen Zhang, Zijian Huang, Yingcong Li, Chenshun Ni, Jiasi Chen, Samet Oymak

Small language models (SLMs) struggle to learn complex reasoning behaviors, especially when high-quality traces are scarce or difficult to learn from. A typical approach for training such models combines a supervised fine-tuning (SFT) stage, often to distill reasoning capabilities from a larger model, followed by a reinforcement learning (RL) stage such as Group Relative Policy Optimization (GRPO). In this paper, we investigate the fundamental limitations of this SFT + RL paradigm and propose methods to overcome them. Using a toy student-expert model over Markov chains, we demonstrate that the SFT + RL strategy can fail completely when (1) the expert's traces are too difficult for the small model to express, or (2) the small model's initialization achieves exponentially sparse rewards as task complexity grows. To address these, we introduce BREAD, a GRPO variant that bridges SFT and RL via partial expert guidance and branch rollouts. When self-generated traces fail, BREAD adaptively inserts short expert prefixes/hints, allowing the small model to complete the rest of the reasoning path, and ensuring that each update includes at least one successful trace. This mechanism both densifies the reward signal and induces a natural learning curriculum. BREAD requires fewer than 40\% of ground-truth traces, consistently outperforming standard GRPO while speeding up the training by about 3$\times$. Importantly, we find that BREAD helps the model solve problems that are otherwise unsolvable by the SFT + RL strategy, highlighting how branch rollouts and expert guidance can aid SLM reasoning.

Deep Learning · Generative Models and Autoencoders

Javier E. Santos, Agnese Marcato, Roman Colman, NIcholas Lubbers, Yen Ting Lin

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result, they are fundamentally ill-suited for applications involving inherently discrete quantities such as particle counts or material units, that are constrained by strict conservation laws like mass conservation, limiting their applicability in scientific workflows. To address this limitation, we propose Discrete Spatial Diffusion (DSD), a framework based on a continuous-time, discrete-state jump stochastic process that operates directly in discrete spatial domains while strictly preserving particle counts in both forward and reverse diffusion processes. By using spatial diffusion to achieve particle conservation, we introduce stochasticity naturally through a discrete formulation. We demonstrate the expressive flexibility of DSD by performing image synthesis, class conditioning, and image inpainting across standard image benchmarks, while exactly conditioning total image intensity. We validate DSD on two challenging scientific applications: porous rock microstructures and lithium-ion battery electrodes, demonstrating its ability to generate structurally realistic samples under strict mass conservation constraints, with quantitative evaluation using state-of-the-art metrics for transport and electrochemical performance.

Social Aspects · Accountability, Transparency and Interpretability

Valérie Costa, Thomas Fel, Ekdeep S Lubana, Bahareh Tolooshams, Demba Ba

Motivated by the hypothesis that neural network representations encode abstract, interpretable features as linearly accessible, approximately orthogonal directions, sparse autoencoders (SAEs) have become a popular tool in interpretability literature. However, recent work has demonstrated phenomenology of model representations that lies outside the scope of this hypothesis, showing signatures of hierarchical, nonlinear, and multi-dimensional features. This raises the question: do SAEs represent features that possess structure at odds with their motivating hypothesis? If not, does avoiding this mismatch help identify said features and gain further insights into neural network representations? To answer these questions, we take a construction-based approach and re-contextualize the popular matching pursuit (MP) algorithm from sparse coding to design MP-SAE—an SAE that unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features. Comparing this architecture with existing SAEs on a mixture of synthetic and natural data settings, we show: (i) hierarchical concepts induce conditionally orthogonal features, which existing SAEs are unable to faithfully capture, and (ii) the nonlinear encoding step of MP-SAE recovers highly meaningful features, helping us unravel shared structure in the seemingly dichotomous representation spaces of different modalities in a vision-language model, hence demonstrating the assumption that useful features are solely linearly accessible is insufficient. We also show that the sequential encoder principle of MP-SAE affords an additional benefit of adaptive sparsity at inference time, which may be of independent interest. Overall, we argue our results provide credence to the idea that interpretability should begin with the phenomenology of representations, with methods emerging from assumptions that fit it.

Applications · Neuroscience, Cognitive Science

Eray Erturk, Saba Hashemi, Maryam Shanechi

Local field potentials (LFPs) can be routinely recorded alongside spiking activity in intracortical neural experiments, measure a larger complementary spatiotemporal scale of brain activity for scientific inquiry, and can offer practical advantages over spikes, including greater long-term stability, robustness to electrode degradation, and lower power requirements. Despite these advantages, recent neural modeling frameworks have largely focused on spiking activity since LFP signals pose inherent modeling challenges due to their aggregate, population-level nature, often leading to lower predictive power for downstream task variables such as motor behavior. To address this challenge, we introduce a cross-modal knowledge distillation framework that transfers high-fidelity representational knowledge from pretrained multi-session spike transformer models to LFP transformer models. Specifically, we first train a teacher spike model across multiple recording sessions using a masked autoencoding objective with a session-specific neural tokenization strategy. We then align the latent representations of the student LFP model to those of the teacher spike model. Our results show that the distilled LFP models consistently outperform single- and multi-session LFP baselines in both fully unsupervised and supervised settings, and can generalize to other sessions without additional distillation while maintaining superior performance. These findings demonstrate that cross-modal knowledge distillation is a powerful and scalable approach for leveraging high-performing spike models to develop more accurate LFP models.

Deep Learning · Generative Models and Autoencoders

Riccardo De Santi, Marin Vlastelica, Ya-Ping Hsieh, Zebang Shen, Niao He, Andreas Krause

Adapting large-scale foundational flow and diffusion generative models to optimize task-specific objectives while preserving prior information is crucial for real-world applications such as molecular design, protein docking, and creative image generation. Existing principled fine-tuning methods aim to maximize the expected reward of generated samples, while retaining knowledge from the pre-trained model via KL-divergence regularization. In this work, we tackle the significantly more general problem of optimizing general utilities beyond average rewards, including risk-averse and novelty-seeking reward maximization, diversity measures for exploration, and experiment design objectives among others. Likewise, we consider more general ways to preserve prior information beyond KL-divergence, such as optimal transport distances and Rényi divergences. To this end, we introduce Flow Density Control (FDC), a simple algorithm that reduces this complex problem to a specific sequence of simpler fine-tuning tasks, each solvable via scalable established methods. We derive convergence guarantees for the proposed scheme under realistic assumptions by leveraging recent understanding of mirror flows. Finally, we validate our method on illustrative settings, text-to-image, and molecular design tasks, showing that it can steer pre-trained generative models to optimize objectives and solve practically relevant tasks beyond the reach of current fine-tuning schemes.

Deep Learning · Generative Models and Autoencoders

Jaesik Yoon, Hyeonseo Cho, Yoshua Bengio, Sungjin Ahn

Diffusion models have recently emerged as a powerful approach for trajectory planning. However, their inherently non-sequential nature limits their effectiveness in long-horizon reasoning tasks at test time. The recently proposed Monte Carlo Tree Diffusion (MCTD) offers a promising solution by combining diffusion with tree-based search, achieving state-of-the-art performance on complex planning problems. Despite its strengths, our analysis shows that MCTD incurs substantial computational overhead due to the sequential nature of tree search and the cost of iterative denoising. To address this, we propose Fast-MCTD, a more efficient variant that preserves the strengths of MCTD while significantly improving its speed and scalability. Fast-MCTD integrates two techniques: Parallel MCTD, which enables parallel rollouts via delayed tree updates and redundancy-aware selection; and Sparse MCTD, which reduces rollout length through trajectory coarsening. Experiments show that Fast-MCTD achieves up to 100× speedup over standard MCTD while maintaining or improving planning performance. Remarkably, it even outperforms Diffuser in inference speed on some tasks, despite Diffuser requiring no search and yielding weaker solutions. These results position Fast-MCTD as a practical and scalable solution for diffusion-based inference-time reasoning.

Deep Learning · Generative Models and Autoencoders

Anindya Sarkar, Binglin Ji, Yevgeniy Vorobeychik

In many scientific and engineering fields, where acquiring high-quality data is expensive—such as medical imaging, environmental monitoring, and remote sensing—strategic sampling of unobserved regions based on prior observations is crucial for maximizing discovery rates within a constrained budget. The rise of powerful generative models, such as diffusion models, has enabled active target discovery in partially observable environments by leveraging learned priors—probabilistic representations that capture underlying structure from data. With guidance from sequentially gathered task-specific observations, these models can progressively refine exploration and efficiently direct queries toward promising regions. However, in domains where learning a strong prior is infeasible due to extremely limited data or high sampling cost (such as rare species discovery, diagnostics for emerging diseases, etc.), these methods struggle to generalize. To overcome this limitation, we propose a novel approach that enables effective active target discovery even in settings with uninformative priors, ensuring robust exploration and adaptability in complex real-world scenarios. Our framework is theoretically principled and draws inspiration from neuroscience to guide its design. Unlike black-box policies, our approach is inherently interpretable, providing clear insights into decision-making. Furthermore, it guarantees a strong, monotonic improvement in prior estimates with each new observation, leading to increasingly accurate sampling and reinforcing both reliability and adaptability in dynamic settings. Through comprehensive experiments and ablation studies across various domains, including species distribution modeling and remote sensing, we demonstrate that our method substantially outperforms baseline approaches.

Deep Learning · Generative Models and Autoencoders

Anindya Sarkar, Binglin Ji, Yevgeniy Vorobeychik

In various scientific and engineering domains, where data acquisition is costly—such as in medical imaging, environmental monitoring, or remote sensing—strategic sampling from unobserved regions, guided by prior observations, is essential to maximize target discovery within a limited sampling budget. In this work, we introduce Diffusion-guided Active Target Discovery (DiffATD), a novel method that leverages diffusion dynamics for active target discovery. DiffATD maintains a belief distribution over each unobserved state in the environment, using this distribution to dynamically balance exploration-exploitation. Exploration reduces uncertainty by sampling regions with the highest expected entropy, while exploitation targets areas with the highest likelihood of discovering the target, indicated by the belief distribution and an incrementally trained reward model designed to learn the characteristics of the target. DiffATD enables efficient target discovery in a partially observable environment within a fixed sampling budget, all without relying on any prior supervised training. Furthermore, DiffATD offers interpretability, unlike existing black-box policies that require extensive supervised training. Through extensive experiments and ablation studies across diverse domains, including medical imaging, species discovery and remote sensing, we show that DiffATD performs significantly better than baselines and competitively with supervised methods that operate under full environmental observability.

Deep Learning · Generative Models and Autoencoders

Gabriel Nobis, Maximilian Springenberg, Arina Belova, Rembert Daems, Christoph Knochenhauer, Manfred Opper, Tolga Birdal, Wojciech Samek

We present *Fractional Diffusion Bridge Models* (FDBM), a novel generative diffusion bridge framework driven by the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of memory effects (correlations in time), long-range dependencies, roughness and anomalous diffusion phenomena that are not captured in standard diffusion or bridge modeling due to the use of Brownian motion (BM). As a remedy, leveraging a recent Markovian approximation (MA-fBM), we construct FDBM that enable tractable inference while preserving the non-Markovian nature of fBM. We prove that the resulting bridge is a coupling-preserving process and leverage it for future state prediction from paired training data. We then extend our formulation to the Schrödinger bridge problem and derive a principled loss function to learn the unpaired data translation. We evaluate FDBM on both tasks: predicting future protein conformations from aligned data, and unpaired image translation. In both settings, FDBM achieves superior performance compared to the Brownian baselines, yielding lower root mean squared deviation (RMSD) of C$_\alpha$ atomic positions in protein structure prediction and lower Fréchet Inception Distance (FID) in unpaired image translation.

Applications · Physics

Ali Can Bekar, Siddhant Agarwal, Christian Hüttig, Nicola Tosi, David Greenberg

For classical PDE solvers, adjusting the spatial resolution and time step offers a trade-off between speed and accuracy. Neural emulators often achieve better speed-accuracy trade-offs by operating accurately on a compact representation of the PDE system. Coarsened PDE fields are a simple and effective representation, but cannot exploit fine spatial scales in the high-fidelity numerical solutions. Alternatively, unstructured latent representations provide efficient autoregressive rollouts, but cannot enforce local interactions or physical laws as inductive biases. To overcome these limitations, we introduce hybrid representations that augment coarsened PDE fields with spatially structured latent variables extracted from high-resolution inputs. Hybrid representations provide efficient rollouts, can be trained on a simple loss defined on coarsened PDE fields, and support hard physical constraints. When predicting fine- and coarse-scale features across multiple PDE emulation tasks, they outperform or match the speed-accuracy trade-offs of the best convolutional, attentional, Fourier operator-based and autoencoding baselines.

Deep Learning · Generative Models and Autoencoders

Jiesong Liu, Xipeng Shen

Image generation requires intensive computations and faces challenges due to long latency. Exploiting redundancy in the input images and intermediate representations throughout the neural network pipeline is an effective way to accelerate image generation. Token merging (ToMe) exploits similarities among input tokens by clustering them and merges similar tokens into one, thus significantly reducing the number of tokens that are fed into the transformer block. This work introduces Fourier Token Merging, a new method for understanding and capitalizing frequency domain for efficient image generation. By introducing frequency token merging, we find that transforming the token into the frequency domain representation for clustering can better exert the ability of clustering based on the underlying redundancy after de-correlation. Through analytical and empirical studies, we demonstrate the benefits of using Fourier clustering over the original time domain clustering. We experimented fourier token merging on the stable diffusion model, and the results show up to 25\% reduction in latency without impairing image quality. The code is available at https://github.com/Fred1031/Fourier-Token-Merging.

Deep Learning · Generative Models and Autoencoders

Xinxin You, Qixin Sun, Chenwei Yan, Xiao Zhang, Chen Ning, Xiangling Fu, Si Liu, Guoping Hu, Shijin Wang, Ji Wu 等

Inconsistent hallucinations remain a major challenge for large language models (LLMs), undermining the accuracy and reliability of fact-based reasoning in real-world applications. Existing approaches often rely on task-specific training or adaptation, such as hand-crafted synthetic datasets for domain tasks or solutions mainly focused on numerical reasoning, thereby limiting generalizability to broader, unseen NLP tasks. Inspired by the structural rigor and logical consistency of programming languages, we observe that fact-based texts can be mapped to programming structures due to their inherent patterns. We further propose FACT, a novel Fact-driven Alternating Code-text Training framework that alternates between text-to-code and code-to-text prediction. FACT is the first task-agnostic paradigm that embeds code and natural language in a shared semantic space, thereby transferring the logical consistency of code to LLM outputs in NLP tasks. Experiments show that with only a small subset of Wiki-40B-en for training, FACT reduces inconsistent hallucinations by 2.7%–8.0% and improves overall performance by 2.5%–6.1% in three leading LLMs and four diverse datasets covering QA and summarization tasks. This framework offers a new perspective on addressing challenging hallucinations in LLMs, contributing to more reliable AI.

Deep Learning · Generative Models and Autoencoders

Marton Havasi, Brian Karrer, Itai Gat, Ricky T. Q. Chen

Autoregressive generative models naturally generate variable-length sequences, while non-autoregressive models struggle, often imposing rigid, token-wise structures. We propose Edit Flows, a non-autoregressive model that overcomes these limitations by defining a discrete flow over sequences through edit operations---insertions, deletions, and substitutions. By modeling these operations within a Continuous-time Markov Chain over the sequence space, Edit Flows enable flexible, position-relative generation that aligns more closely with the structure of sequence data. Our training method leverages an expanded state space with auxiliary variables, making the learning process efficient and tractable. Empirical results show that Edit Flows outperforms both autoregressive and mask models on image captioning and significantly outperforms the mask construction in text and code generation.

Deep Learning · Generative Models and Autoencoders

Zongle Huang, Lei Zhu, ZongYuan Zhan, Ting Hu, Weikai Mao, Xianzhi Yu, Yongpan Liu, Tianyu Zhang

Large Language Models (LLMs) have achieved remarkable success across many applications, with Mixture of Experts (MoE) models demonstrating great potential. Compared to traditional dense models, MoEs achieve better performance with less computation. Speculative decoding (SD) is a widely used technique to accelerate LLM inference without accuracy loss, but it has been considered efficient only for dense models. In this work, we first demonstrate that, under medium batch sizes, MoE surprisingly benefits more from SD than dense models. Furthermore, as MoE becomes sparser -- the prevailing trend in MoE designs -- the batch size range where SD acceleration is expected to be effective becomes broader. To quantitatively understand tradeoffs involved in SD, we develop a reliable modeling based on theoretical analyses. While current SD research primarily focuses on improving acceptance rates of algorithms, changes in workload and model architecture can still lead to degraded SD acceleration even with high acceptance rates. To address this limitation, we introduce a new metric 'target efficiency' that characterizes these effects, thus helping researchers identify system bottlenecks and understand SD acceleration more comprehensively. For scenarios like private serving, this work unveils a new perspective to speed up MoE inference, where existing solutions struggle. Experiments on different GPUs show up to 2.29x speedup for Qwen2-57B-A14B at medium batch sizes and validate our theoretical predictions.

Deep Learning · Generative Models and Autoencoders

Dejan Stancevic, Florian Handke, Luca Ambrogioni

The practical performance of generative diffusion models depends on the appropriate choice of the noise scheduling function, which can also be equivalently expressed as a time reparameterization. In this paper, we present a time scheduler that selects sampling points based on entropy rather than uniform time spacing, ensuring that each point contributes an equal amount of information to the final generation. We prove that this time reparameterization does not depend on the initial choice of time. Furthermore, we provide a tractable exact formula to estimate this \emph{entropic time} for a trained model using the training loss without substantial overhead. Alongside the entropic time, inspired by the optimality results, we introduce a rescaled entropic time. In our experiments with mixtures of Gaussian distributions and ImageNet, we show that using the (rescaled) entropic times greatly improves the inference performance of trained models. In particular, we found that the image quality in pretrained EDM2 models, as evaluated by FID and FD-DINO scores, can be substantially increased by the rescaled entropic time reparameterization without increasing the number of function evaluations, with greater improvements in the few NFEs regime. Code is available at \url{https://github.com/DejanStancevic/Entropic-Time-Schedulers-for-Generative-Diffusion-Models}.

Deep Learning · Generative Models and Autoencoders

Zhengkai Lin, Zhihang Fu, Ze Chen, Chao Chen, Liang Xie, Wenxiao Wang, Deng Cai, Zheng Wang, Jieping Ye

Human cognition is theorized to operate in two modes: fast, intuitive System 1 thinking and slow, deliberate System 2 thinking. While current Large Reasoning Models (LRMs) excel at System 2 thinking, their inability to perform fast thinking leads to high computational overhead and latency. In this work, we enable LRMs to approximate human intelligence through dynamic thinking speed adjustment, optimizing accuracy-efficiency trade-offs. Our approach addresses two key questions: (1) how to control thinking speed in LRMs, and (2) when to adjust it for optimal performance. For the first question, we identify the steering vector that governs slow-fast thinking transitions in LRMs' representation space. Using this vector, we achieve the first representation editing-based test-time scaling effect, outperforming existing prompt-based scaling methods. For the second question, we apply real-time difficulty estimation to signal reasoning segments of varying complexity. Combining these techniques, we propose the first reasoning strategy that enables fast processing of easy steps and deeper analysis for complex reasoning. Without any training or additional cost, our plug-and-play method yields an average +1.3\% accuracy with -8.6\% token usage across leading LRMs and advanced reasoning benchmarks. All of our algorithms are implemented based on vLLM and are expected to support broader applications and inspire future research.

Deep Learning · Generative Models and Autoencoders

Cai Zhou, Chenyu Wang, Dinghuai Zhang, Shangyuan Tong, Yifei Wang, Stephen Bates, Tommi Jaakkola

In this paper we introduce Hierarchical Diffusion Language Models (HDLM) -- a novel family of discrete diffusion models for language modeling. HDLM builds on a hierarchical vocabulary where low-level tokens with detailed semantics are surjectively mapped to high-level tokens with coarse-grained meanings. In the forward process, each token is independently perturbed to its higher-level ancestor with more abstract semantics according to the scheduler, while in the reverse process the model progressively predicts the next, more detailed semantics. Taken together, HDLM provides a general time-varying next semantic scale prediction process for language modeling. We derive closed-form expressions for the diffusion Evidence Lower Bound (ELBO), and show that HDLM can be implemented in a flexible manner while including the existing MDLM as a special case. We also propose practical training techniques based on the insights. Extensive text generation experiments validate the effectiveness of HDLM, which demonstrates consistently lower validation and generative perplexity than baselines.

Deep Learning · Generative Models and Autoencoders

Qingming LIU, Zhen Liu, Dinghuai Zhang, Kui Jia

Generating high-quality and photorealistic 3D assets remains a longstanding challenge in 3D vision and computer graphics. Although state-of-the-art generative models, such as diffusion models, have made significant progress in 3D generation, they often fall short of human-designed content due to limited ability to follow instructions, align with human preferences, or produce realistic textures, geometries, and physical attributes. In this paper, we introduce Nabla-R2D3, a highly effective and sample-efficient reinforcement learning alignment framework for 3D-native diffusion models using 2D rewards. Built upon the recently proposed Nabla-GFlowNet method for reward finetuning, our Nabla-R2D3 enables effective adaptation of 3D diffusion models through pure 2D reward feedback. Extensive experiments show that, unlike naive finetuning baselines which either fail to converge or suffer from overfitting, Nabla-R2D3 consistently achieves higher rewards and reduced prior forgetting within few finetuning steps.

Deep Learning · Generative Models and Autoencoders

Keshigeyan Chandrasegaran, Michael Poli, Dan Fu, Dongjun Kim, Lea M. Hadzic, Manling Li, Agrim Gupta, Stefano Massaroli, Azalia Mirhoseini, Juan Carlos Niebles 等

Designing model architectures requires decisions such as selecting operators (e.g., attention, convolution) and configurations (e.g., depth, width). However, evaluating the impact of these decisions on model quality requires costly pretraining, limiting architectural investigation. Inspired by how new software is built on existing code, we ask: can new architecture designs be studied using pretrained models? To this end, we present *grafting*, a simple approach for editing pretrained diffusion transformers (DiTs) to materialize new architectures under small compute budgets. Informed by our analysis of activation behavior and attention locality, we construct a testbed based on the DiT-XL/2 design to study the impact of grafting on model quality. Using this testbed, we develop a family of hybrid designs via grafting: replacing softmax attention with gated convolution, local attention, and linear attention, and replacing MLPs with variable expansion ratio and convolutional variants. Notably, many hybrid designs achieve good quality (FID: 2.38–2.64 vs. 2.27 for DiT-XL/2) using $<2$% pretraining compute. We then graft a text-to-image model (PixArt-$\Sigma$), achieving a 1.43$\times$ speedup with less than a 2% drop in GenEval score. Finally, we present a case study that restructures DiT-XL/2 by converting every pair of sequential transformer blocks into parallel blocks via grafting. This reduces model depth by 2$\times$ and yields better quality (FID: 2.77) than other models of comparable depth. Together, we show that new diffusion model designs can be explored by grafting pretrained DiTs, with edits ranging from operator replacement to architecture restructuring. Code and grafted models: https://grafting.stanford.edu.

Deep Learning · Generative Models and Autoencoders

Sebastian Wagner-Carena, Aizhan Akhmetzhanova, Sydney Erickson

In the natural sciences, a common challenge is to disentangle distinct, unknown sources from observations. Examples of this source separation task include deblending galaxies in a crowded field, distinguishing the activity of individual neurons from overlapping signals, and separating seismic events from the ambient background. Traditional analyses often rely on simplified source models that fail to accurately reproduce the data. Recent advances have shown that diffusion models can directly learn complex prior distributions from noisy, incomplete data. In this work, we show that diffusion models can solve the source separation problem without explicit assumptions about the source. Our method relies only on multiple views, or the property that different sets of observations contain different linear transformations of the unknown sources. We show that our method succeeds even when no source is individually observed and the observations are noisy, incomplete, and vary in resolution. The learned diffusion models enable us to sample from the source priors, evaluate the probability of candidate sources, and draw from the joint posterior of our sources given an observation. We demonstrate the effectiveness of our method on a range of synthetic problems as well as real-world galaxy observations.