Yongxin Chen

Niket Agarwal, Arslan Ali, Maciej Bala et al. · nvidia

Physical AI needs to be trained digitally first. It needs a digital twin of itself, the policy model, and a digital twin of the world, the world model. In this paper, we present the Cosmos World Foundation Model Platform to help developers build customized world models for their Physical AI setups. We position a world foundation model as a general-purpose world model that can be fine-tuned into customized world models for downstream applications. Our platform covers a video curation pipeline, pre-trained world foundation models, examples of post-training of pre-trained world foundation models, and video tokenizers. To help Physical AI builders solve the most critical problems of our society, we make Cosmos open-source and our models open-weight with permissive licenses available via https://github.com/nvidia-cosmos/cosmos-predict1.

Arslan Ali, Junjie Bai, Maciej Bala et al. · nvidia

We introduce [Cosmos-Predict2.5], the latest generation of the Cosmos World Foundation Models for Physical AI. Built on a flow-based architecture, [Cosmos-Predict2.5] unifies Text2World, Image2World, and Video2World generation in a single model and leverages [Cosmos-Reason1], a Physical AI vision-language model, to provide richer text grounding and finer control of world simulation. Trained on 200M curated video clips and refined with reinforcement learning-based post-training, [Cosmos-Predict2.5] achieves substantial improvements over [Cosmos-Predict1] in video quality and instruction alignment, with models released at 2B and 14B scales. These capabilities enable more reliable synthetic data generation, policy evaluation, and closed-loop simulation for robotics and autonomous systems. We further extend the family with [Cosmos-Transfer2.5], a control-net style framework for Sim2Real and Real2Real world translation. Despite being 3.5$\times$ smaller than [Cosmos-Transfer1], it delivers higher fidelity and robust long-horizon video generation. Together, these advances establish [Cosmos-Predict2.5] and [Cosmos-Transfer2.5] as versatile tools for scaling embodied intelligence. To accelerate research and deployment in Physical AI, we release source code, pretrained checkpoints, and curated benchmarks under the NVIDIA Open Model License at https://github.com/nvidia-cosmos/cosmos-predict2.5 and https://github.com/nvidia-cosmos/cosmos-transfer2.5. We hope these open resources lower the barrier to adoption and foster innovation in building the next generation of embodied intelligence.

Yuchen Zhu, Jing Shi, Chongjian Ge et al.

Autoregressive (AR) large language models (LLMs) have achieved broad practical success, but sequential decoding remains a key bottleneck for low-latency deployment. Recent efficient-inference work has progressed along two axes: reducing the cost of each model invocation through efficient architectures, and reducing serial decoding steps through parallel generation. Hybrid attention backbones address the former, while diffusion language models (dLLMs) pursue the latter via iterative parallel denoising. Combining these advantages remains challenging: AR-to-dLLM conversion often fails to preserve seed-checkpoint capability, and hybrid-attention recurrent states and masking constraints make diffusion training and serving nontrivial. We present FLARE, a systematic conversion framework for hybrid-attention LLMs. Our analysis identifies transfer data quality as the primary determinant of capability preservation, outweighing loss formulation and attention-mask design. The resulting framework combines a token-equal AR-and-diffusion objective, hardware-aware kernels, and unified inference, enabling one checkpoint to support both AR-style verified decoding and diffusion-style parallel denoising. Starting from strong AR checkpoints with limited post-training data, FLARE is competitive with leading open-source dLLMs across model scales and delivers consistent throughput gains over open-source dLLM baselines in single-GPU concurrent serving. Our results further suggest that practical dLLMs are limited not only by decoding algorithms, but also by transfer data quality and the training inefficiency of current block-diffusion objectives, motivating joint design of data, objectives, architectures, and inference systems.

Qinsheng Zhang, Yongxin Chen

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate $50k$ images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at https://github.com/qsh-zh/deis

Qinsheng Zhang, Molei Tao, Yongxin Chen

Our goal is to extend the denoising diffusion implicit model (DDIM) to general diffusion models~(DMs) besides isotropic diffusions. Instead of constructing a non-Markov noising process as in the original DDIM, we examine the mechanism of DDIM from a numerical perspective. We discover that the DDIM can be obtained by using some specific approximations of the score when solving the corresponding stochastic differential equation. We present an interpretation of the accelerating effects of DDIM that also explains the advantages of a deterministic sampling scheme over the stochastic one for fast sampling. Building on this insight, we extend DDIM to general DMs, coined generalized DDIM (gDDIM), with a small but delicate modification in parameterizing the score network. We validate gDDIM in two non-isotropic DMs: Blurring diffusion model (BDM) and Critically-damped Langevin diffusion model (CLD). We observe more than 20 times acceleration in BDM. In the CLD, a diffusion model by augmenting the diffusion process with velocity, our algorithm achieves an FID score of 2.26, on CIFAR10, with only 50 number of score function evaluations~(NFEs) and an FID score of 2.86 with only 27 NFEs. Code is available at https://github.com/qsh-zh/gDDIM

Haotian Xue, Chumeng Liang, Xiaoyu Wu et al. · gatech

While generative diffusion models excel in producing high-quality images, they can also be misused to mimic authorized images, posing a significant threat to AI systems. Efforts have been made to add calibrated perturbations to protect images from diffusion-based mimicry pipelines. However, most of the existing methods are too ineffective and even impractical to be used by individual users due to their high computation and memory requirements. In this work, we present novel findings on attacking latent diffusion models (LDM) and propose new plug-and-play strategies for more effective protection. In particular, we explore the bottleneck in attacking an LDM, discovering that the encoder module rather than the denoiser module is the vulnerable point. Based on this insight, we present our strategy using Score Distillation Sampling (SDS) to double the speed of protection and reduce memory occupation by half without compromising its strength. Additionally, we provide a robust protection strategy by counterintuitively minimizing the semantic loss, which can assist in generating more natural perturbations. Finally, we conduct extensive experiments to substantiate our findings and comprehensively evaluate our newly proposed strategies. We hope our insights and protective measures can contribute to better defense against malicious diffusion-based mimicry, advancing the development of secure AI systems. The code is available in https://github.com/xavihart/Diff-Protect

Yongxin Chen, Tryphon T. Georgiou, Allen Tannenbaum

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models. Basically, we study such models on a certain submanifold of probability densities with certain structure. Different aspects of this framework are discussed and several examples are presented to illustrate the results. This method represents our first attempt to study optimal transport problems for more general probability densities with structures.

Ernest K. Ryu, Yongxin Chen, Wuchen Li et al.

In many applications such as color image processing, data has more than one piece of information associated with each spatial coordinate, and in such cases the classical optimal mass transport (OMT) must be generalized to handle vector-valued or matrix-valued densities. In this paper, we discuss the vector and matrix optimal mass transport and present three contributions. We first present a rigorous mathematical formulation for these setups and provide analytical results including existence of solutions and strong duality. Next, we present a simple, scalable, and parallelizable methods to solve the vector and matrix-OMT problems. Finally, we implement the proposed methods on a CUDA GPU and present experiments and applications.

Yongxin Chen, Tryphon Georgiou, Allen Tannenbaum

We consider damped stochastic systems in a controlled (time-varying) quadratic potential and study their transition between specified Gibbs-equilibria states in finite time. By the second law of thermodynamics, the minimum amount of work needed to transition from one equilibrium state to another is the difference between the Helmholtz free energy of the two states and can only be achieved by a reversible (infinitely slow) process. The minimal gap between the work needed in a finite-time transition and the work during a reversible one, turns out to equal the square of the optimal mass transport (Wasserstein-2) distance between the two end-point distributions times the inverse of the duration needed for the transition. This result, in fact, relates non-equilibrium optimal control strategies (protocols) to gradient flows of entropy functionals via and the Jordan-Kinderlehrer-Otto scheme. The purpose of this paper is to introduce ideas and results from the emerging field of stochastic thermodynamics in the setting of classical regulator theory, and to draw connections and derive such fundamental relations from a control perspective in a multivariable setting.

Yongxin Chen, Tryphon T. Georgiou, Michele Pavon et al.

We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with certain initial and final marginals. The random evolution is selected to be closest to a prior measure on paths in the relative entropy sense, i.e., a Schroedinger bridge between the two marginals. This is an atypical stochastic control problem where the control consists in suitably modifying the transition mechanism. The prior can incorporate cost of traversing edges or allocate equal probability to all paths of equal length connecting any two given nodes, i.e., a uniform measure on paths. This latter choice relies on the so-called Ruelle-Bowen random walk and gives rise to a scheduling that tends to utilize all paths as uniformly as the topology allows. Thus, when the Ruelle-Bowen law is taken as prior, the transportation plan tends to lessen congestion and ensure a level of robustness. We show that the Ruelle-Bowen law is itself a Schroedinger bridge albeit with a prior that is not a probability measure. The paradigm of Schroedinger bridges as a mechanism for scheduling transport on networks can be adapted to graphs that are not strongly connected as well as to weighted graphs. The latter leads to transportation plans that effect a compromise between robustness and transportation cost.

Yongxin Chen, Giovanni Conforti, Tryphon T. Georgiou

The aim of this article is to introduce and address the problem to smoothly interpolate (empirical) probability measures. To this end, we lift the concept of a spline curve from the setting of points in a Euclidean space that that of probability measures, using the framework of optimal transport.

Byoungwoo Park, Utkarsh A. Mishra, Jaemoo Choi et al.

Diffusion models provide strong priors for generating structured data, but many tasks require outputs beyond the scale on which these models are typically trained. Compositional generation addresses this by composing overlapping local plans from a pretrained short-horizon prior into a long-horizon output. However, standard composition primarily enforces agreement between neighboring local plans, yielding local consistency without directly specifying the global structure of the full composition. As a result, locally compatible plans may still form an implausible route, task sequence, or temporal evolution. Existing methods improve global coherence by repeatedly propagating local consistency signals or by adding inference-time optimization, but these procedures become expensive as the number or dimensionality of local plans increases. We propose Coarse-to-Fine Compositional Diffusion (CoFi), an inference-time sampler that separates global structure formation from local detail refinement. CoFi first aligns local denoised estimates around a shared coarse structure, producing a global scaffold that captures the long-range task-level arrangement. It then diffuses this scaffold to an intermediate noise level and denoises it with the same pretrained local prior, restoring local fine structure while preserving the scaffold-induced global coherence. Across long-horizon robotic planning, panoramic image generation, and long video generation, CoFi not only improves both global coherence and local sample quality over prior compositional baselines, but also requires 2-8x fewer denoiser evaluations.

Qinsheng Zhang, Jiaming Song, Xun Huang et al.

We present DiffCollage, a compositional diffusion model that can generate large content by leveraging diffusion models trained on generating pieces of the large content. Our approach is based on a factor graph representation where each factor node represents a portion of the content and a variable node represents their overlap. This representation allows us to aggregate intermediate outputs from diffusion models defined on individual nodes to generate content of arbitrary size and shape in parallel without resorting to an autoregressive generation procedure. We apply DiffCollage to various tasks, including infinite image generation, panorama image generation, and long-duration text-guided motion generation. Extensive experimental results with a comparison to strong autoregressive baselines verify the effectiveness of our approach.

Yongxin Chen, Johan Karlsson

We consider the problems of tracking an ensemble of indistinguishable agents with linear dynamics based only on output measurements. In this setting, the dynamics of the agents can be modeled by distribution flows in the state space and the measurements correspond to distributions in the output space. In this paper we formulate the corresponding state estimation problem using optimal mass transport theory with prior linear dynamics, and the optimal solution gives an estimate of the state trajectories of the ensemble. For general distributions of systems this can be formulated as a convex optimization problem which is computationally feasible with when the number of state dimensions is low. In the case where the marginal distributions are Gaussian, the problem is reformulated as a semidefinite programming and can be efficiently solved for tracking systems with a large number of states.

Kaiwen Zheng, Yongxin Chen, Hanzi Mao et al.

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20$\times$ speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs in text generation. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that it lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

Zeqian Long, Ozgur Kara, Haotian Xue et al. · gatech

Image-to-video (I2V) generation has the potential for societal harm because it enables the unauthorized animation of static images to create realistic deepfakes. While existing defenses effectively protect against static image manipulation, extending these to I2V generation remains underexplored and non-trivial. In this paper, we systematically analyze why modern I2V models are highly robust against naive image-level adversarial attacks (i.e., immunization). We observe that the video encoding process rapidly dilutes the adversarial noise across future frames, and the continuous text-conditioned guidance actively overrides the intended disruptive effect of the immunization. Building on these findings, we propose the Immune2V framework which enforces temporally balanced latent divergence at the encoder level to prevent signal dilution, and aligns intermediate generative representations with a precomputed collapse-inducing trajectory to counteract the text-guidance override. Extensive experiments demonstrate that Immune2V produces substantially stronger and more persistent degradation than adapted image-level baselines under the same imperceptibility budget.

Wei Guo, Molei Tao, Yongxin Chen · gatech

We consider the outstanding problem of sampling from an unnormalized density that may be non-log-concave and multimodal. To enhance the performance of simple Markov chain Monte Carlo (MCMC) methods, techniques of annealing type have been widely used. However, quantitative theoretical guarantees of these techniques are under-explored. This study takes a first step toward providing a non-asymptotic analysis of annealed MCMC. Specifically, we establish, for the first time, an oracle complexity of $\widetilde{O}\left(\frac{dβ^2{\cal A}^2}{\varepsilon^6}\right)$ for the simple annealed Langevin Monte Carlo algorithm to achieve $\varepsilon^2$ accuracy in Kullback-Leibler divergence to the target distribution $π\propto{\rm e}^{-V}$ on $\mathbb{R}^d$ with $β$-smooth potential $V$. Here, ${\cal A}$ represents the action of a curve of probability measures interpolating the target distribution $π$ and a readily sampleable distribution.

Yongxin Chen, Tryphon T. Georgiou, Michele Pavon

The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. The framework is that of mean-field and of cooperative games. A terminal cost is used to accomplish the task; we establish that the map between terminal costs and terminal probability distributions is onto. Our approach relies on and extends the theory of optimal mass transport and its generalizations.

Lama Moukheiber, Caleb M. Yeung, Haotian Xue et al. · gatech

Spatial reasoning and visual grounding are core capabilities for vision-language models (VLMs), yet most medical VLMs produce predictions without transparent reasoning or spatial evidence. Existing benchmarks also evaluate VLMs on isolated 2D images, overlooking the volumetric nature of clinical imaging, where findings can span multiple frames or appear on only a few slices. We introduce Spatially Grounded MRI Visual Question Answering (SGMRI-VQA), a 41,307-pair benchmark for multi-frame, spatially grounded reasoning on volumetric MRI. Built from expert radiologist annotations in the fastMRI+ dataset across brain and knee studies, each QA pair includes a clinician-aligned chain-of-thought trace with frame-indexed bounding box coordinates. Tasks are organized hierarchically across detection, localization, counting/classification, and captioning, requiring models to jointly reason about what is present, where it is, and across which frames it extends. We benchmark 10 VLMs and show that supervised fine-tuning of Qwen3-VL-8B with bounding box supervision consistently improves grounding performance over strong zero-shot baselines, indicating that targeted spatial supervision is an effective path toward grounded clinical reasoning.

Qinsheng Zhang, Jiaming Song, Yongxin Chen

Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating state-of-the-art performance. However, existing high-order EI-based sampling algorithms rely on degenerate EI solvers, resulting in inferior error bounds and reduced accuracy in contrast to the theoretically anticipated results under optimal settings. This situation makes the sampling quality extremely vulnerable to seemingly innocuous design choices such as timestep schedules. For example, an inefficient timestep scheduler might necessitate twice the number of steps to achieve a quality comparable to that obtained through carefully optimized timesteps. To address this issue, we reevaluate the design of high-order differential solvers for DMs. Through a thorough order analysis, we reveal that the degeneration of existing high-order EI solvers can be attributed to the absence of essential order conditions. By reformulating the differential equations in DMs and capitalizing on the theory of exponential integrators, we propose refined EI solvers that fulfill all the order conditions, which we designate as Refined Exponential Solver (RES). Utilizing these improved solvers, RES exhibits more favorable error bounds theoretically and achieves superior sampling efficiency and stability in practical applications. For instance, a simple switch from the single-step DPM-Solver++ to our order-satisfied RES solver when Number of Function Evaluations (NFE) $=9$, results in a reduction of numerical defects by $25.2\%$ and FID improvement of $25.4\%$ (16.77 vs 12.51) on a pre-trained ImageNet diffusion model.

Zishun Liu, Yongxin Chen

We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based control, it remains unclear whether data-driven approaches, which bypass the system identification step, can solve the problem. In this work, we present a novel data-driven online adaptive control algorithm to address this online control problem. Our algorithm leverages the behavioral systems theory to learn a non-parametric system representation and then adopts a perturbation-based controller updated by online gradient descent. We prove that our algorithm guarantees an $\tmO(T^{2/3})$ regret bound with high probability, which matches the best-known regret bound for this problem. Furthermore, we extend our algorithm and performance guarantee to the cases with output feedback.

Utkarsh A. Mishra, Yongxin Chen

The ability to manipulate objects in a desired configurations is a fundamental requirement for robots to complete various practical applications. While certain goals can be achieved by picking and placing the objects of interest directly, object reorientation is needed for precise placement in most of the tasks. In such scenarios, the object must be reoriented and re-positioned into intermediate poses that facilitate accurate placement at the target pose. To this end, we propose a reorientation planning method, ReorientDiff, that utilizes a diffusion model-based approach. The proposed method employs both visual inputs from the scene, and goal-specific language prompts to plan intermediate reorientation poses. Specifically, the scene and language-task information are mapped into a joint scene-task representation feature space, which is subsequently leveraged to condition the diffusion model. The diffusion model samples intermediate poses based on the representation using classifier-free guidance and then uses gradients of learned feasibility-score models for implicit iterative pose-refinement. The proposed method is evaluated using a set of YCB-objects and a suction gripper, demonstrating a success rate of 95.2% in simulation. Overall, our study presents a promising approach to address the reorientation challenge in manipulation by learning a conditional distribution, which is an effective way to move towards more generalizable object manipulation. For more results, checkout our website: https://utkarshmishra04.github.io/ReorientDiff.

Endong Gu, Yongxin Chen, Hao Wen et al.

This paper proposes LCFL, a novel clustering metric for evaluating clients' data distributions in federated learning. LCFL aligns with federated learning requirements, accurately assessing client-to-client variations in data distribution. It offers advantages over existing clustered federated learning methods, addressing privacy concerns, improving applicability to non-convex models, and providing more accurate classification results. LCFL does not require prior knowledge of clients' data distributions. We provide a rigorous mathematical analysis, demonstrating the correctness and feasibility of our framework. Numerical experiments with neural network instances highlight the superior performance of LCFL over baselines on several clustered federated learning benchmarks.

Zelin Zhao, Petr Molodyk, Haotian Xue et al. · gatech

In this paper, we present Laplacian multiscale flow matching (LapFlow), a novel framework that enhances flow matching by leveraging multi-scale representations for image generative modeling. Our approach decomposes images into Laplacian pyramid residuals and processes different scales in parallel through a mixture-of-transformers (MoT) architecture with causal attention mechanisms. Unlike previous cascaded approaches that require explicit renoising between scales, our model generates multi-scale representations in parallel, eliminating the need for bridging processes. The proposed multi-scale architecture not only improves generation quality but also accelerates the sampling process and promotes scaling flow matching methods. Through extensive experimentation on CelebA-HQ and ImageNet, we demonstrate that our method achieves superior sample quality with fewer GFLOPs and faster inference compared to single-scale and multi-scale flow matching baselines. The proposed model scales effectively to high-resolution generation (up to 1024$\times$1024) while maintaining lower computational overhead.

Jiaming Liang, Yongxin Chen

We study sampling problems associated with non-convex potentials that meanwhile lack smoothness. In particular, we consider target distributions that satisfy either logarithmic-Sobolev inequality or Poincaré inequality. Rather than smooth, the potentials are assumed to be semi-smooth or the summation of multiple semi-smooth functions. We develop a sampling algorithm that resembles proximal algorithms in optimization for this challenging sampling task. Our algorithm is based on a special case of Gibbs sampling known as the alternating sampling framework (ASF). The key contribution of this work is a practical realization of the ASF based on rejection sampling in the non-convex and semi-smooth setting. This work extends the recent algorithm in \cite{LiaChe21,LiaChe22} for non-smooth/semi-smooth log-concave distribution to the setting with non-convex potentials. In almost all the cases of sampling considered in this work, our proximal sampling algorithm achieves better complexity than all existing methods.

Alexis M. H. Teter, Yongxin Chen, Abhishek Halder

Schrödinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schrödinger bridge problems, in both classical and in the linear system settings, is via contractive fixed point recursions. These recursions can be seen as dynamic versions of the well-known Sinkhorn iterations, and under mild assumptions, they solve the so-called Schrödinger systems with guaranteed linear convergence. In this work, we study a priori estimates for the contraction coefficients associated with the convergence of respective Schrödinger systems. We provide new geometric and control-theoretic interpretations for the same. Building on these newfound interpretations, we point out the possibility of improved computation for the worst-case contraction coefficients of linear SBPs by preconditioning the endpoint support sets.

Rahul Singh, Yongxin Chen

Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each convolution layer they perform low-pass filtering of the input features followed by a learnable linear transformation. Their extension to signed graphs with positive as well as negative links imposes multiple issues including computational irregularities and ambiguous frequency interpretation, making the design of computationally efficient low pass filters challenging. In this paper, we address these issues via spectral analysis of signed graphs and propose two different signed graph neural networks, one keeps only low-frequency information and one also retains high-frequency information. We further introduce magnetic signed Laplacian and use its eigendecomposition for spectral analysis of directed signed graphs. We test our methods for node classification and link sign prediction tasks on signed graphs and achieve state-of-the-art performances.

Xiaochen Du, Juno Nam, Jaemoo Choi et al.

Sampling from discrete distributions with multiple modes and energy barriers is fundamental to machine learning and computational physics. Recent discrete neural samplers like MDNS suffer from mode collapse and fail to sample high-energy barrier regions between modes, which is critical for free energy estimation and understanding phase transitions. We propose Metadynamics Discrete Neural Sampler (MetaDNS), a general framework integrating well-tempered metadynamics into discrete diffusion or autoregressive samplers. By maintaining an adaptive, history-dependent bias potential along selected low-dimensional coordinates, MetaDNS forces exploration of previously inaccessible regions, enabling free energy reconstruction infeasible with standard neural samplers due to a lack of high-energy samples. On challenging low-temperature benchmarks including Ising, Potts, and the copper-gold binary alloy, MetaDNS reproduces the thermodynamic distribution. Compared to MCMC-based metadynamics, MetaDNS also achieves comparable exploration requiring fewer bias deposition steps.

Zelin Zhao, Bo Yuan, Jaemoo Choi et al.

We present $\textbf{Research Math Agents (RMA)}$, an agentic framework for automated reasoning on research-level mathematical problems. Unlike prior studies centered on competition mathematics or formal theorem proving, RMA targets research-level mathematical problems that require long-horizon reasoning, literature grounding, and iterative proof refinement. RMA decomposes research-level proof solving into specialized modules for problem analysis, literature search and understanding, fair comparison, knowledge-bank construction, and proof verification, all coordinated by initializer, proposer, and verifier agents through a shared structured memory. Within this unified framework, these agents operate in a multi-role, multi-round workflow, collaboratively generating, refining, and verifying candidate proofs through iterative feedback. We evaluate RMA on the First Proof benchmark, which consists of ten research-level problems contributed by expert mathematicians across diverse domains. Through comprehensive expert evaluation, RMA outperforms strong baselines on the First Proof benchmark, including GPT-5.2R and Aletheia, solving eight out of ten research problems and producing more logically sound and readable proofs. Our comprehensive ablation studies further show that performance gains arise from the interaction of structured reasoning modules, iterative refinement, and verifier-based feedback, rather than any single component. Our solutions and implementations will be made publicly available upon acceptance.

Zhihan Yang, Wei Guo, Shuibai Zhang et al.

While diffusion has drawn considerable recent attention from the language modeling community, continuous diffusion has appeared less scalable than discrete approaches. To challenge this belief we revisit Plaid, a likelihood-based continuous diffusion language model (DLM), and construct RePlaid by aligning the architecture of Plaid with modern discrete DLMs. In this unified setting, we establish the first scaling law for continuous DLMs that rivals discrete DLMs: RePlaid exhibits a compute gap of only $20\times$ compared to autoregressive models, outperforms Duo while using fewer parameters, and outperforms MDLM in the over-trained regime. We benchmark RePlaid against recent continuous DLMs: on OpenWebText, RePlaid achieves a new state-of-the-art PPL bound of $22.1$ among continuous DLMs and superior generation quality. These results suggest that continuous diffusion, when trained via likelihood, is a highly competitive and scalable alternative to discrete DLMs. Moreover, we offer theoretical insights to understand the advantage of likelihood-based training. We show that optimizing the noise schedule to minimize the ELBO's variance naturally yields linear cross-entropy (information loss) over time. This evenly distributes denoising difficulty without any case-specific time reparameterization. In addition, we find that optimizing embeddings via likelihood creates structured geometries and drives the most significant likelihood gain.

Haotian Xue, Qi Chen, Zhonghao Wang et al.

Video diffusion models achieve strong frame-level fidelity but still struggle with motion coherence, dynamics and realism, often producing jitter, ghosting, or implausible dynamics. A key limitation is that the standard denoising MSE objective provides no direct supervision on temporal consistency, allowing models to achieve low loss while still generating poor motion. We propose MoGAN, a motion-centric post-training framework that improves motion realism without reward models or human preference data. Built atop a 3-step distilled video diffusion model, we train a DiT-based optical-flow discriminator to differentiate real from generated motion, combined with a distribution-matching regularizer to preserve visual fidelity. With experiments on Wan2.1-T2V-1.3B, MoGAN substantially improves motion quality across benchmarks. On VBench, MoGAN boosts motion score by +7.3% over the 50-step teacher and +13.3% over the 3-step DMD model. On VideoJAM-Bench, MoGAN improves motion score by +7.4% over the teacher and +8.8% over DMD, while maintaining comparable or even better aesthetic and image-quality scores. A human study further confirms that MoGAN is preferred for motion quality (52% vs. 38% for the teacher; 56% vs. 29% for DMD). Overall, MoGAN delivers significantly more realistic motion without sacrificing visual fidelity or efficiency, offering a practical path toward fast, high-quality video generation. Project webpage is: https://xavihart.github.io/mogan.

Yuchen Zhu, Wei Guo, Jaemoo Choi et al. · gatech

We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function $π\propto\mathrm{e}^{-U}$ is known up to a normalizing constant, which is an important task in fields such as statistical physics, machine learning, combinatorial optimization, etc. To better address this challenging task when the state space has a large cardinality and the distribution is multi-modal, we propose $\textbf{M}$asked $\textbf{D}$iffusion $\textbf{N}$eural $\textbf{S}$ampler ($\textbf{MDNS}$), a novel framework for training discrete neural samplers by aligning two path measures through a family of learning objectives, theoretically grounded in the stochastic optimal control of the continuous-time Markov chains. We validate the efficiency and scalability of MDNS through extensive experiments on various distributions with distinct statistical properties, where MDNS learns to accurately sample from the target distributions despite the extremely high problem dimensions and outperforms other learning-based baselines by a large margin. A comprehensive study of ablations and extensions is also provided to demonstrate the efficacy and potential of the proposed framework. Our code is available at https://github.com/yuchen-zhu-zyc/MDNS.

Haotian Xue, Yongxin Chen · gatech

Adversarial examples for diffusion models are widely used as solutions for safety concerns. By adding adversarial perturbations to personal images, attackers can not edit or imitate them easily. However, it is essential to note that all these protections target the latent diffusion model (LDMs), the adversarial examples for diffusion models in the pixel space (PDMs) are largely overlooked. This may mislead us to think that the diffusion models are vulnerable to adversarial attacks like most deep models. In this paper, we show novel findings that: even though gradient-based white-box attacks can be used to attack the LDMs, they fail to attack PDMs. This finding is supported by extensive experiments of almost a wide range of attacking methods on various PDMs and LDMs with different model structures, which means diffusion models are indeed much more robust against adversarial attacks. We also find that PDMs can be used as an off-the-shelf purifier to effectively remove the adversarial patterns that were generated on LDMs to protect the images, which means that most protection methods nowadays, to some extent, cannot protect our images from malicious attacks. We hope that our insights will inspire the community to rethink the adversarial samples for diffusion models as protection methods and move forward to more effective protection. Codes are available in https://github.com/xavihart/PDM-Pure.

Jaemoo Choi, Yuchen Zhu, Wei Guo et al.

Reinforcement learning has been widely applied to diffusion and flow models for visual tasks such as text-to-image generation. However, these tasks remain challenging because diffusion models have intractable likelihoods, which creates a barrier for directly applying popular policy-gradient type methods. Existing approaches primarily focus on crafting new objectives built on already heavily engineered LLM objectives, using ad hoc estimators for likelihood, without a thorough investigation into how such estimation affects overall algorithmic performance. In this work, we provide a systematic analysis of the RL design space by disentangling three factors: i) policy-gradient objectives, ii) likelihood estimators, and iii) rollout sampling schemes. We show that adopting an evidence lower bound (ELBO) based model likelihood estimator, computed only from the final generated sample, is the dominant factor enabling effective, efficient, and stable RL optimization, outweighing the impact of the specific policy-gradient loss functional. We validate our findings across multiple reward benchmarks using SD 3.5 Medium, and observe consistent trends across all tasks. Our method improves the GenEval score from 0.24 to 0.95 in 90 GPU hours, which is $4.6\times$ more efficient than FlowGRPO and $2\times$ more efficient than the SOTA method DiffusionNFT without reward hacking.

Wei Guo, Yuchen Zhu, Xiaochen Du et al.

Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is $\mathit{state}\text{-}\mathit{space~agnostic}$, and introduce $\mathbf{discrete~ASBS}$, a unified framework that extends AM and adjoint Schrödinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.

Yongxin Chen, Zhiyuan Jiang, Chao Zhang et al.

Traditional database fuzzing techniques primarily focus on syntactic correctness and general SQL structures, leaving critical yet obscure DBMS features, such as system-level modes (e.g., GTID), programmatic constructs (e.g., PROCEDURE), advanced process commands (e.g., KILL), largely underexplored. Although rarely triggered by typical inputs, these features can lead to severe crashes or security issues when executed under edge-case conditions. In this paper, we present FuzzySQL, a novel LLM-powered adaptive fuzzing framework designed to uncover subtle vulnerabilities in DBMS special features. FuzzySQL combines grammar-guided SQL generation with logic-shifting progressive mutation, a novel technique that explores alternative control paths by negating conditions and restructuring execution logic, synthesizing structurally and semantically diverse test cases. To further ensure deeper execution coverage of the back end, FuzzySQL employs a hybrid error repair pipeline that unifies rule-based patching with LLM-driven semantic repair, enabling automatic correction of syntactic and context-sensitive failures. We evaluate FuzzySQL across multiple DBMSs, including MySQL, MariaDB, SQLite, PostgreSQL and Clickhouse, uncovering 64 vulnerabilities, 27 of which are tied to under-tested DBMS special features. As of this writing, 60 cases have been confirmed with 9 assigned CVE identifiers, 31 already fixed by vendors, and additional vulnerabilities scheduled to be patched in upcoming releases. Our results highlight the limitations of conventional fuzzers in semantic feature coverage and demonstrate the potential of LLM-based fuzzing to discover deeply hidden bugs in complex database systems.

Anqi Dong, Yongxin Chen, Karl H. Johansson et al.

Steering large-scale swarms in only a few control updates is challenging because real systems operate in sampled-data form: control inputs are updated intermittently and applied over finite intervals. In this regime, the natural object is not an instantaneous velocity field, but a finite-window control quantity that captures the system response over each sampling interval. Inspired by MeanFlow, we introduce a control-space learning framework for swarm steering under linear time-invariant dynamics. The learned object is the coefficient that parameterizes the finite-horizon minimum-energy control over each interval. We show that this coefficient admits both an integral representation and a local differential identity along bridge trajectories, which leads to a simple stop-gradient training objective. At implementation time, the learned coefficient is used directly in sampled-data updates, so the prescribed dynamics and actuation map are respected by construction. The resulting framework provides a scalable approach to few-step swarm steering that is consistent with the sampled-data structure of real control systems.

Zhaoyuan Gu, Yipu Chen, Zimeng Chai et al.

Humanoid loco-manipulation requires coordinated high-level motion plans with stable, low-level whole-body execution under complex robot-environment dynamics and long-horizon tasks. While diffusion policies (DPs) show promise for learning from demonstrations, deploying them on humanoids poses critical challenges: the motion planner trained offline is decoupled from the low-level controller, leading to poor command tracking, compounding distribution shift, and task failures. The common approach of scaling demonstration data is prohibitively expensive for high-dimensional humanoid systems. To address this challenge, we present REFINE-DP (REinforcement learning FINE-tuning of Diffusion Policy), a hierarchical framework that jointly optimizes a DP high-level planner and an RL-based low-level loco-manipulation controller. The DP is fine-tuned via a PPO-based diffusion policy gradient to improve task success rate, while the controller is simultaneously updated to accurately track the planner's evolving command distribution, reducing the distributional mismatch that degrades motion quality. We validate REFINE-DP on a humanoid robot performing loco-manipulation tasks, including door traversal and long-horizon object transport. REFINE-DP achieves an over $90\%$ success rate in simulation, even in out-of-distribution cases not seen in the pre-trained data, and enables smooth autonomous task execution in real-world dynamic environments. Our proposed method substantially outperforms pre-trained DP baselines and demonstrates that RL fine-tuning is key to reliable humanoid loco-manipulation. https://refine-dp.github.io/REFINE-DP/

Yuchen Zhu, Wei Guo, Jaemoo Choi et al.

Diffusion large language models (dLLMs) are promising alternatives to autoregressive large language models (AR-LLMs), as they potentially allow higher inference throughput. Reinforcement learning (RL) is a crucial component for dLLMs to achieve comparable performance with AR-LLMs on important tasks, such as reasoning. However, RL algorithms that are well-suited for dLLMs' unique characteristics have yet to be developed. This paper proposes Distribution Matching Policy Optimization (DMPO), a principled and theoretically grounded RL fine-tuning method specifically designed to enhance the reasoning capabilities of dLLMs by matching the dLLM policy distribution to the optimal, reward-tilted one through cross-entropy optimization. We identify a key challenge in the implementation with a small training batch size and propose several effective solutions through a novel weight baseline subtraction technique. DMPO exhibits superior performance on multiple reasoning benchmarks without supervised fine-tuning, with an accuracy improvement of up to $42.9\%$ over previously SOTA baselines and $55.8\%$ over the base model, underscoring the effectiveness of the distribution matching framework. Our code is available at https://github.com/yuchen-zhu-zyc/DMPO.

Asmaa Eldesoukey, Yongxin Chen, Abhishek Halder

The mean-field Schrödinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline. Unlike the standard Schrödinger bridge, the dynamical constraint for MFSB is the mean-field limit of a population of interacting agents with controls. It serves as a natural model for large-scale multi-agent systems. The MFSB is computationally challenging because the nonlocal interaction makes the problem nonconvex. We propose a generalization of the Hopf-Cole transform for MFSB and, building on it, design a Sinkhorn-type recursive algorithm to solve the associated system of integro-PDEs. Under mild assumptions on the interaction potential, we discuss convergence guarantees for the proposed algorithm. We present numerical examples with repulsive and attractive interactions to illustrate the theoretical contributions.

Karthik Shaji, Sreeranj Jayadevan, Bo Yuan et al.

We present an optimal-control-based particle filtering method for state estimation in hybrid systems that undergo intermittent contact with their environments. We follow the path integral filtering framework that exploits the duality between the smoothing problem and optimal control. We leverage saltation matrices to map out the uncertainty propagation during contact events for hybrid systems. The resulting path integral optimal control problem allows for a state estimation algorithm robust to outlier effects, flexible to non-Gaussian noise distributions, that also handles the challenging contact dynamics in hybrid systems. This work offers a computationally efficient and reliable estimation algorithm for hybrid systems with stochastic dynamics. We also present extensive experimental results demonstrating that our approach consistently outperforms strong baselines across multiple settings.

Haotian Xue, Yunhao Ge, Yu Zeng et al. · gatech

Vision-Language Models (VLMs) have demonstrated impressive world knowledge across a wide range of tasks, making them promising candidates for embodied reasoning applications. However, existing benchmarks primarily evaluate the embodied reasoning ability of VLMs through multiple-choice questions based on image annotations -- for example, selecting which trajectory better describes an event in the image. In this work, we introduce the Point-It-Out (PIO) benchmark, a novel benchmark designed to systematically assess the embodied reasoning abilities of VLMs through precise visual grounding. We propose a hierarchical evaluation protocol spanning three stages (S1: referred-object localization, S2: task-driven pointing, and S3: visual trace prediction), with data collected from critical domains for embodied intelligence, including indoor, kitchen, driving, and robotic manipulation scenarios. Extensive experiments with over ten state-of-the-art VLMs reveal several interesting findings. For example, strong general-purpose models such as GPT-4o, while excelling on many benchmarks (e.g., language, perception, and reasoning), underperform compared to some open-source models in precise visual grounding; models such as MoLMO perform well in S1 and S2 but struggle in S3, where requires grounding combined with visual trace planning.

Haotian Xue, Alexandre Araujo, Bin Hu et al.

Neural networks are known to be susceptible to adversarial samples: small variations of natural examples crafted to deliberately mislead the models. While they can be easily generated using gradient-based techniques in digital and physical scenarios, they often differ greatly from the actual data distribution of natural images, resulting in a trade-off between strength and stealthiness. In this paper, we propose a novel framework dubbed Diffusion-Based Projected Gradient Descent (Diff-PGD) for generating realistic adversarial samples. By exploiting a gradient guided by a diffusion model, Diff-PGD ensures that adversarial samples remain close to the original data distribution while maintaining their effectiveness. Moreover, our framework can be easily customized for specific tasks such as digital attacks, physical-world attacks, and style-based attacks. Compared with existing methods for generating natural-style adversarial samples, our framework enables the separation of optimizing adversarial loss from other surrogate losses (e.g., content/smoothness/style loss), making it more stable and controllable. Finally, we demonstrate that the samples generated using Diff-PGD have better transferability and anti-purification power than traditional gradient-based methods. Code will be released in https://github.com/xavihart/Diff-PGD

Hongzhe Yu, Zinuo Chang, Yongxin Chen

Stochastic trajectory optimization methods like STOMP enable planning with non-differentiable costs, offering substantial flexibility over gradient-based approaches. We show that STOMP implicitly minimizes the KL divergence from a Boltzmann trajectory distribution, revealing an elegant Variational Inference (VI) structure underlying its updates. Building on this insight, we propose the \textit{Proximal Inference for Stochastic Trajectory Optimization} (PISTO) algorithm that stabilizes the updates by augmenting the objective with a KL regularization between successive Gaussian proposals. This proximal formulation admits a trust-region interpretation and yields closed-form mean updates computable as expectations under a surrogate distribution. We estimate these expectations via importance-weighted Monte Carlo sampling, producing a simple, derivative-free algorithm that inherits STOMP's ability to handle non-differentiable and discontinuous costs without modification. On robot arm motion planning benchmarks, PISTO achieves an 89\% success rate -- outperforming CHOMP (63\%) and STOMP (68\%) -- while producing shorter, smoother paths at twice the speed of competing stochastic methods. We further validate PISTO on contact-rich MuJoCo locomotion and manipulation tasks, where it consistently outperforms both CEM and MPPI baselines in reward.

Liqian Ma, Zishun Liu, Glen Chou et al.

We study feedback motion planning for continuous-time stochastic nonlinear systems under signal temporal logic (STL) specifications. We propose a framework that synthesizes control policies for chance-constrained STL trajectory optimization problems, with the goal of ensuring that the closed-loop stochastic system satisfies a given STL formula with high probability (e.g., 99.99\%). Our approach is based on a predicate erosion strategy that transforms the intractable stochastic problem into a deterministic STL trajectory optimization problem with tightened STL formula constraints. The amount of erosion is determined by a probabilistic reachable tube (PRT) that bounds the deviation between the stochastic trajectory and an associated nominal trajectory. To compute such bounds, we leverage contraction theory and feedback design, and develop several tracking controllers. This yields a complete feedback motion planning pipeline which can be implemented by numerical optimizations. We demonstrate the efficacy and versatility of the proposed framework through simulations on several robotic systems and through experiments on a real-world quadrupedal robot, and show that it is less conservative and achieves higher specification satisfaction probability than representative baselines.

Yinuo Ren, Haoxuan Chen, Yuchen Zhu et al. · gatech, stanford

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the development of efficient inference algorithms. Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as $τ$-leaping. While exact methods suffer from unpredictable inference time and redundant function evaluations, $τ$-leaping is limited by its first-order accuracy. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models, enabling larger step sizes while reducing error. We rigorously analyze the proposed schemes and establish the second-order accuracy of the $θ$-trapezoidal method in KL divergence. Empirical evaluations on GPT-2 level text and ImageNet-level image generation tasks demonstrate that our method achieves superior sample quality compared to existing approaches under equivalent computational constraints.

Zelin Zhao, Xinyu Gong, Bangya Liu et al.

Achieving precise camera control in video generation remains challenging, as existing methods often rely on camera pose annotations that are difficult to scale to large and dynamic datasets and are frequently inconsistent with depth estimation, leading to train-test discrepancies. We introduce CETCAM, a camera-controllable video generation framework that eliminates the need for camera annotations through a consistent and extensible tokenization scheme. CETCAM leverages recent advances in geometry foundation models, such as VGGT, to estimate depth and camera parameters and converts them into unified, geometry-aware tokens. These tokens are seamlessly integrated into a pretrained video diffusion backbone via lightweight context blocks. Trained in two progressive stages, CETCAM first learns robust camera controllability from diverse raw video data and then refines fine-grained visual quality using curated high-fidelity datasets. Extensive experiments across multiple benchmarks demonstrate state-of-the-art geometric consistency, temporal stability, and visual realism. Moreover, CETCAM exhibits strong adaptability to additional control modalities, including inpainting and layout control, highlighting its flexibility beyond camera control. The project page is available at https://sjtuytc.github.io/CETCam_project_page.github.io/.

Bo Yuan, Zelin Zhao, Petr Molodyk et al.

Large language models have recently enabled text-to-CAD systems that synthesize parametric CAD programs (e.g., CadQuery) from natural language prompts. In practice, however, geometric descriptions can be under-specified or internally inconsistent: critical dimensions may be missing and constraints may conflict. Existing fine-tuned models tend to reactively follow user instructions and hallucinate dimensions when the text is ambiguous. To address this, we propose a proactive agentic framework for text-to-CadQuery generation, named ProCAD, that resolves specification issues before code synthesis. Our framework pairs a proactive clarifying agent, which audits the prompt and asks targeted clarification questions only when necessary to produce a self-consistent specification, with a CAD coding agent that translates the specification into an executable CadQuery program. We fine-tune the coding agent on a curated high-quality text-to-CadQuery dataset and train the clarifying agent via agentic SFT on clarification trajectories. Experiments show that proactive clarification significantly improves robustness to ambiguous prompts while keeping interaction overhead low. ProCAD outperforms frontier closed-source models, including Claude Sonnet 4.5, reducing the mean Chamfer distance by 79.9 percent and lowering the invalidity ratio from 4.8 percent to 0.9 percent. Our code and datasets will be made publicly available.

Kaiwen Zheng, Yongxin Chen, Huayu Chen et al.

While likelihood-based generative models, particularly diffusion and autoregressive models, have achieved remarkable fidelity in visual generation, the maximum likelihood estimation (MLE) objective, which minimizes the forward KL divergence, inherently suffers from a mode-covering tendency that limits the generation quality under limited model capacity. In this work, we propose Direct Discriminative Optimization (DDO) as a unified framework that integrates likelihood-based generative training and GAN-type discrimination to bypass this fundamental constraint by exploiting reverse KL and self-generated negative signals. Our key insight is to parameterize a discriminator implicitly using the likelihood ratio between a learnable target model and a fixed reference model, drawing parallels with the philosophy of Direct Preference Optimization (DPO). Unlike GANs, this parameterization eliminates the need for joint training of generator and discriminator networks, allowing for direct, efficient, and effective finetuning of a well-trained model to its full potential beyond the limits of MLE. DDO can be performed iteratively in a self-play manner for progressive model refinement, with each round requiring less than 1% of pretraining epochs. Our experiments demonstrate the effectiveness of DDO by significantly advancing the previous SOTA diffusion model EDM, reducing FID scores from 1.79/1.58/1.96 to new records of 1.30/0.97/1.26 on CIFAR-10/ImageNet-64/ImageNet 512x512 datasets without any guidance mechanisms, and by consistently improving both guidance-free and CFG-enhanced FIDs of visual autoregressive models on ImageNet 256x256.

Georgiy A. Bondar, Asmaa Eldesoukey, Yongxin Chen et al.

Solutions to the Schrödinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the dynamic Sinkhorn recursion has become a standard approach. The mathematical engine behind this approach is the Hopf-Cole transform that recasts the conditions for optimality into a system of boundary-coupled linear PDEs. Recent works pointed out that for the control-affine Schrödinger bridge problem, this exact linearity via Hopf-Cole transform, and thus the standard Sinkhorn recursion, apply only if the control and noise channels are proportional. When the channels do not match, the Hopf-Cole-transformed PDEs remain nonlinear, and no algorithm is available to solve the same. We advance the state-of-the-art by designing a Sinkhorn recursion with memory that leverages the structure of these nonlinear PDEs, and demonstrate how it solves the control-affine Schrödinger bridge problem with input and noise channel mismatch. We prove the local stability of the proposed algorithm.