Results for “diffusion priors”

Repos, models and tools

Papers

arXiv cs.CVSep 25
PhoenixSR: Generative Heterogeneous Distillation Unleashes Efficient Models for Real-World Super-Resolution
Xin Di, Mingyu Shi, Yuanfei Bao, Long Peng, Yue Zhao +5
Real-world image super-resolution (SR) requires recovering perceptually realistic high-resolution images from complex low-resolution observations while preserving faithful content. Diffusion-based SR benefits from strong generative priors but incurs substantial computational overhead, whereas feed-forward CNN and Transformer SR models are efficient yet often struggle to recover realistic high-frequency details. This motivates a natural question: can diffusion priors be transferred to existing diffusion-free SR networks without introducing diffusion components at inference time? To this end, we propose PhoenixSR, a generative heterogeneous distillation framework that transfers diffusion priors to independently designed feed-forward SR networks through score-based distribution matching. Rather than aligning heterogeneous features or imitating sampled diffusion outputs, PhoenixSR uses the pretrained diffusion model as distribution-level supervision, while paired SR supervision preserves reconstruction fidelity. To make distribution matching effective for fidelity-sensitive SR, we introduce Heterogeneous Distribution Adaptation, which adapts the target score to the SR domain,…
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arXiv cs.LGSep 28
GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priors
Wangqian Chen, Hao Wang, Yumeng Zhang, Jiajia Guo, Junting Chen +1
Active grounding of a frozen diffusion prior requires jointly determining where new measurements should be taken and how they should be used to refine the current reconstruction. Posterior-ensemble-based methods can estimate acquisition utility from generated samples, but require repeated ensemble generation as observations accumulate and capture posterior geometry only through empirical statistics. This paper proposes GPARA, which learns a context-dependent graph surrogate over diffusion prediction residuals, inducing an explicitly reusable posterior response operator that propagates measurement innovations to unobserved variables and evaluates candidate measurements through weighted posterior-risk reduction. Under the matched surrogate, we show that the same response operator also determines expected one-step acquisition benefit and yields an analytic ranking consistent with expected reconstruction improvement. A bounded learned residual calibrates the analytic utility to account for surrogate mismatch, while a small prior ensemble is generated once and reconditioned to update risk weights without repeated diffusion posterior sampling during acquisition. Experiments on two…
PDF
arXiv cs.CLOct 9
Rethinking the Roles of Diffusion and Decoding: Predictive-State Flows for Parallel Language Generation
Jinjin He, Xinsong Feng, Lucheng Fu, Sinan Wang, Bo Zhu +1
In continuous diffusion language models (DLMs), latents generated by the diffusion prior are mapped almost deterministically to tokens, either by a decoder or through a token embedding matrix. Unlike in image generation, where visual details can vary continuously, the diffusion prior must capture fine-grained discrete token choices in continuous space, which can make the joint latent distribution difficult to model. We argue that generative roles should instead be divided: the diffusion prior should generate high-level predictive information, while the decoder should resolve the remaining token-level choices. Based on this view, we introduce Predictive-State Flows (PSF), which partitions a sequence into blocks and associates each block with a predictive state computed solely from the preceding context. A rectified-flow prior generates the sequence of predictive states, after which a block-causal decoder generates all blocks in parallel, autoregressively only within each block. This design reduces diffusion from L token-level states to K << L predictive states and reduces token-level sequential depth to L/K. On unconditional OpenWebText generation, a 197M-parameter model with K=8…
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arXiv stat.MLOct 7
Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
Dai Hai Nguyen, Duc Dung Nguyen
Split Gibbs sampling (SGS) is a popular framework for posterior sampling in Bayesian imaging inverse problems. It decouples a Gaussian data-fidelity term from a complex prior through an auxiliary variable, so the data variable is updated exactly and only the prior-side conditional is hard to sample. Existing samplers treat this conditional in one of two ways. Plug-and-play SGS runs a multi-step diffusion denoiser at every iteration, which is expensive and lacks non-asymptotic guarantees. Langevin-within-SGS takes cheap overdamped Langevin steps but needs many iterations. We propose RED-KLwSGS, which keeps the exact Gaussian update for the data variable and updates the auxiliary variable with underdamped (kinetic) Langevin diffusions driven by a one-shot denoising score, at the same per-iteration cost as Langevin-within-SGS. We prove non-asymptotic Wasserstein-2 convergence in continuous and discrete time for strongly log-concave priors. We also introduce Joint-RED-KLwSGS, which applies kinetic Langevin diffusions to both variables. Experiments with Denoising diffusion probabilistic models as diffusion priors on FFHQ and ImageNet datasets show faster convergence and high-quality…
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arXiv cs.LGOct 7
Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps
So Takao, Gregory David Bellchambers, Luke Ye, Sanmitra Ghosh, Michalis Michaelides
Pretrained diffusion models are powerful priors for inverse problems, but posterior sampling under nonlinear, non-differentiable forward models remain hard. We introduce diffusion waltz, an MCMC method using SDEdit-style noising-denoising as a proposal, corrected via Metropolis-Hastings for exact posterior sampling without prior evaluation. We further propose injecting observations into the proposal while preserving exactness, using a gradient-free ensemble Kalman update. On a non-differentiable Navier-Stokes initial condition recovery task, diffusion waltz outperforms existing baselines across different noise and nonlinearity regimes.
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arXiv eess.SPSep 24
Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
Yi Zhang, Rui Guo, Mengchu Xu, Zhaofeng Liu, Yonina C. Eldar
Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.
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arXiv cs.LGOct 9
When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors
Adarsh Jamadandi, Nicolas Keriven, Aline Roumy
Discrete graph diffusion models corrupt graph structure through independent edge updates with a Markovian noise model. Combined with the exchangeability requirement on the output distribution, the terminal prior is necessarily an Erdős--Rényi (E-R) random graph. This has a fundamental consequence for unconditional graph generation without node features: in the large graph limit, any GNN denoiser applied to an E-R graph approximately outputs an E-R graph, making effective denoising difficult. In practice, generated graphs fail to recover meaningful node heterogeneity and higher-order structure. Previous models introduced specialized node features to compensate, framing this as an expressivity problem, while the role of the prior remained unexamined. We instead address the root cause by introducing the Latent Sociability Prior (LSP) and a join} diffusion process that co-evolves latent node sociability variables and graph structure, removing edge independence while preserving exchangeability. Unlike existing latent graph diffusion methods, the sociability mechanism requires no complex encoder: its sole role is to guide edge updates and preserve node heterogeneity throughout the…
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arXiv cs.LGOct 10
Pro-t-VAE: Closed-Form Student's t Mixtures for Robust Prototype Discovery
Zhikang Xu, Jiarui Xing, Jian Wang
We present a robust deep generative framework for unsupervised image prototype discovery, built on a heavy-tailed Student's t mixture prior, that bridges statistical robustness and mathematical tractability. Existing generative approaches typically rely on noise-prone Gaussian priors or computationally intensive diffusion models; neither simultaneously provides explicit latent structure nor exact analytic optimization. While diffusion models can yield strong priors, iterative sampling and intractable likelihoods limit scalability and interpretability for prototype discovery. We address these issues by constructing a Student's t latent space via a Bayesian scale-mixture formulation. This yields a fully closed-form augmented ELBO for unsupervised Student's t mixture variational autoencoders, which, to our knowledge, is the first such objective applied to robust image prototype discovery, avoiding biased variational approximations and high computational costs in prior heavy-tailed or diffusion-based frameworks. Treating precision as a latent variable automatically modulates each data point's influence, downweighting outliers to learn a data-dependent measure of trust. The result is…
PDF
arXiv cs.ROOct 5
P3: Persistent Particle Planning for Constrained Diffusion Control
Hikmet Simsir, Mahyar Fardinfar, Ozgur S. Oguz
Diffusion models provide expressive priors over trajectories, but adapting these priors to test-time constraints requires maintaining feasibility and consistency across successive control decisions. We introduce Persistent Particle Planning (P3), a sequential Monte Carlo framework for diffusion control that maintains a weighted population of candidate plans across replanning steps. At each control step, P3 shifts and partially re-noises the candidate trajectories, refines them under the latest observation, and uses constraint-aware weighting and resampling to select among alternative continuations without retraining the diffusion model. We consider denoising and replanning as one Feynman--Kac particle system and analyze it under an idealized repair. We prove that the re-noising depth controls how reliably a kept plan stays on its route, and that keeping a rare, well-separated route takes far fewer plans than rediscovering it by sampling from scratch. Experiments under multiple test-time constraint configurations show that population reuse reduces route switching and improves success without constraint violations. Because P3 refines earlier plans instead of redrawing them, it also…
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arXiv cs.ROOct 9
Akule: Fast and Scalable Multi-Robot Motion Planning via Sparse Interaction Diffusion
Manav Vora, Gokul Puthumanaillam, Aditya Penumarti, Jane Shin, Melkior Ornik
Diffusion models provide expressive trajectory priors for multi-robot motion planning (MRMP), but scaling them to large teams requires coordinating individual motions without expensive joint computation. We introduce Akule, a sparse interaction diffusion framework that augments a frozen single-robot prior with three learned modules: a reusable pairwise correction model $R_φ$, a contextual selector $U_ψ$ that determines which corrections to evaluate, and a composer $G_ω$ that combines their effects through context-dependent signed weights. This decomposition separates which interactions merit computation from how their effects should be combined into coordinated denoising updates. We train $R_φ$ using matched pairwise trajectory optimizations, then learn $G_ω$ and $U_ψ$ from physically optimized joint trajectories without requiring a prescribed ground-truth interaction graph. The resulting joint proposals are passed to a downstream search-based planner for validation and repair. Across diverse MRMP benchmarks, Akule achieves competitive planning success, complete-planner speedups of up to $25\times$, zero-shot population transfer, and successful planning with up to $256$ robots.…
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arXiv cs.CVOct 19▲ 26
RoAR-VAE: Improving Latent Diffusability through Robust Prediction
Yang Yue, Fangyun Wei, Yitong Wang, Jinjing Zhao, Henry Zheng +2
An effective visual tokenizer must preserve image fidelity while producing latents that downstream diffusion models can learn efficiently. Prior work improves latent diffusability through semantic alignment or joint tokenizer--diffusion training. Revisiting REPA-E, a representative approach, we find that removing its diffusion objective and dedicated generative blocks while retaining semantic prediction from corrupted latents yields comparable downstream generation performance under a matched setting. This observation motivates a general principle of robust prediction: generation-relevant information should remain recoverable from corrupted latents. We instantiate this principle with two complementary objectives. RobustAlign predicts pretrained semantic features from corrupted latents to preserve high-level structure, while RobustRecon reconstructs the clean image to retain fine-grained spatial and appearance information. Together, they form Robust Alignment and Reconstruction VAE (RoAR-VAE). Our analysis suggests that robust prediction improves diffusability by making useful information more accessible in high-variance latent directions, which diffusion models tend to learn…
Code
arXiv cs.LGOct 3
Backward-Consistent Diffusion Sampling for Sparsely Observed PDE Inverse Problems
Yida Pan, Muhammad H. Ashiq, Chanyong Jung, Yixuan Jia, Jonah M. Miller +2
Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for which generative machine learning methods (e.g., diffusion models) have become a leading way to encode the prior. Recent state-of-the-art diffusion solvers lift these priors to function spaces, finding a physics-consistent reconstruction in the output space of the diffusion denoiser. We prove that, in a discontinuous PDE setting, output space methods can result in failure to appropriately minimize the unobserved error with the correct coefficient field. Consequently, we propose Function space Backward-Consistent Sampling (FunBCS), an input space optimization approach for solving PDE problems which aims to find the best input such that the denoiser reconstruction is physics-consistent. We then prove that FunBCS appropriately minimizes the unobserved error, unlike output space optimization methods. Per our theoretical analysis, we also provide insights on how to dynamically allocate the number of input space optimization steps used throughout the sampling process. Our evaluations, across four PDE inverse problems (including the…
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arXiv cs.AISep 21
Unsupervised Brain Anomaly Detection as a Bayesian Inverse Problem with Diffusion Prior
Hugues Roy, Reuben Dorent, Ninon Burgos
Unsupervised anomaly detection (UAD) aims to localize abnormal regions in medical scans without pixel-level annotations. A typical strategy seeks to reconstruct a pseudo-healthy image that preserves subject-specific anatomy. Recently, diffusion models have been proposed to perform UAD. However, these methods rely on heuristic noise schedules or synthetic corruptions to balance subject-specificity and anomaly removal. In this work, we propose an alternative formulation of UAD as a Bayesian inverse problem under a diffusion prior. First, we introduce a latent spatial anomaly mask that models pixel-wise consistency between a test image and its latent corresponding pseudo-healthy image. Then, we propose an approximation of the unknown generation process that links healthy anatomy, anomalies, and the observed image, enabling a well-defined likelihood within the Bayesian framework. Building on recent advances in diffusion-based inverse problem methods, we jointly infer the pseudo-healthy image and the anomaly mask via annealed posterior sampling. We evaluate our approach on FDG PET (ADNI) and FLAIR MRI (BraTS 2021), demonstrating improved anomaly localization performance compared to…
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arXiv stat.MLOct 13
Structure-aware Bayesian full waveform inversion via diffusion-regularized Stein variational gradient descent
Chao Li, Mrinal K. Sen, Sergey Fomel, Yangkang Chen
Full waveform inversion (FWI) is a powerful tool for high-resolution subsurface model reconstruction, but it remains highly nonlinear and ill-posed, especially when the initial model is inaccurate or the acquired data are noisy and incomplete. Annealed Stein variational gradient descent (ASVGD) provides a particle-based Bayesian framework for FWI by approximating the posterior distribution with an ensemble of velocity models, thereby enabling uncertainty quantification beyond a single deterministic solution. However, conventional ASVGD-FWI commonly relies on simple handcrafted priors, such as Gaussian or smoothing assumptions, which are often insufficient to represent complex geological structures. To address this limitation, we introduce a learned diffusion model (DM) as an implicit regularization mechanism within the ASVGD-FWI framework. Instead of explicitly evaluating the diffusion prior density, the trained diffusion model acts as a learned geological projection operator that guides updated particles toward the distribution of plausible velocity models. In this way, the proposed method combines data consistency from FWI, posterior diversity from ASVGD, and structural realism…
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arXiv cs.CVOct 13
Recasting DiT for Extreme Image Compression with Hierarchical Visual Priors
Yunuo Chen, Jingnan Gao, Bing He, Jinjing Zhao, Chuqin Zhou +4
Pretrained diffusion models provide powerful generative priors for extreme image compression, but their stochastic, iterative generation processes are not designed to decode compressed representations directly. We present PrismCodec, which recasts a pretrained Diffusion Transformer (DiT) as a bitstream-grounded one-step generative decoder. PrismCodec uses the decoded representation in two complementary roles: a projected codec state defines the starting state for generation, while hierarchical visual priors derived from the same decoded latent provide semantic and structural guidance. To bridge the gap between stochastic, iterative generation and deterministic one-step decoding, we develop a progressive adaptation strategy. We first learn codec-conditioned transport from a noisy neighborhood centered on the codec state, distill it into a one-step mapping, and finally anneal the source perturbation to zero during end-to-end optimization. The resulting decoder reconstructs deterministically from the received representation without additional conditioning bits. Across Kodak, CLIC, and DIV2K, PrismCodec consistently improves rate-perception performance over prior generative codecs,…
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arXiv cs.LGOct 9
Spanning Diffusion and Flow-based Posterior Sampling via Exact Gaussian Conditioning
Teo Deveney, Lea Bogensperger, Hok Shing Wong
Flow-matching and diffusion models are increasingly used as priors for linear inverse problems, however, most methods are bespoke to one class of trajectory prior. Plug-and-play methods have been proposed, however these implicitly decorrelate the guided trajectory, resulting in broad priors that can struggle when data is sparse. This work proposes $β$-Flow: a general plug-and-play method indexed by a correlation parameter $β$ that generalises over flow, diffusion, and decorrelated priors, and a confidence parameter $κ$ that controls how strongly the path distribution is enforced. Each step requires only one forward evaluation of a denoising network, followed by a Gaussian conditioning step. This step is an exact Kalman update that is not dependent on network gradients. We show that many existing guided samplers can be interpreted as instances or approximations of our method, each implicitly using a different trajectory prior and operator in place of the Kalman gain. From this viewpoint, we provide a qualitative comparison of methods in terms of their implicit biases and assumptions. We demonstrate consistently state-of-the-art level performance across 7 inverse problems over 4…
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arXiv cs.CVOct 13▲ 3
H-DDCM: Hadamard Codebooks for Fast Generative Image and Video Compression
Or Ronai, Vladimir Kulikov, Tomer Michaeli
Training-free diffusion-based compression methods repurpose the generative priors of a diffusion or a flow model to compress data without retraining them as task-specific codecs. Recent codebook-based approaches such as Turbo-DDCM achieve strong perceptual quality at ultra-low bitrates, but their reliance on dense Gaussian codebooks remains costly in both memory and computation, and scales poorly with the large latent dimensions of modern image and video generators. Their combinatorial bitstream encoding further becomes computationally heavy at this scale. We introduce H-DDCM, a scalable generative compression framework that replaces Gaussian codebooks with implicit randomized Hadamard dictionaries. The fast Walsh-Hadamard transform allows for implicitly synthesizing full-dimensional dictionaries with $O(d \log d)$ compute for projection and reconstruction and $O(d)$ memory, without materializing the full-dimensional dictionary. We further introduce an efficient table-free lexicographic coding scheme that makes combinatorial encoding practical at larger dimensions. Beyond images, we adapt the framework to an autoregressive video flow model and develop a streaming compression…
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arXiv cs.CVOct 13
$\mathrm{S}^3$-PnP: Plug-and-Play Denoising for Scientific Imaging with Self-Supervised Score Priors
Yukun Cui, Jiangshe Zhang, Shuang Xu, Lilun Deng, Haowen Bai +4
Modern image restoration methods increasingly rely on large-scale supervised training, yet clean targets are often prohibitively difficult to obtain in scientific imaging modalities such as hyperspectral imaging (HSI) and magnetic resonance imaging (MRI). Plug-and-play ADMM (PnP-ADMM) with pretrained diffusion priors offers a promising alternative, but the learned prior distribution can mismatch both the target scientific image distribution and the distribution of ADMM denoiser inputs induced by dual feedback. To mitigate these mismatches, we propose $\mathrm{S}^3$-PnP, a self-supervised plug-and-play restoration framework that learns a score prior directly from observation-derived ADMM intermediate states, without clean training targets or externally pretrained weights. Specifically, the learned score corrects the input to the analytical prior update, combining observation-driven corrections with analytical regularization. We further analyze the convergence and reconstruction error of the corrected ADMM algorithm assuming an ideal score and quadratic data fidelity. Experiments on reference-guided HSI restoration, single-image HSI denoising, and MRI denoising demonstrate…
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arXiv cs.LGSep 27
Perturb-and-Solve: Efficient Learned-Operator Conditioning for Latent Diffusion Inverse Problems
Abduragim Shtanchaev, Arip Asadulaev, Luiza Labazanova, Aidar Alimbayev, Karim Salta +1
Latent diffusion models serve as powerful priors for solving inverse problems in image restoration, such as deblurring, inpainting, and super-resolution. Current methods have a trade-off between generality and efficiency. Solvers that are restricted to a fixed set of degradation operators are fast and efficient. Methods that support arbitrary degradation operators are slow and require gradients through the diffusion network. To break this bottleneck, we introduce PASEO (Perturb-And-Solve for Efficient Operator conditioning), a method that uses a small (1M parameters) learned network to degrade diffusion model predictions in latent space. PASEO supports learned degradation operators without back-propagating through the diffusion network. We efficiently sample reconstructions from an approximate posterior by combining the diffusion model's prediction with the observed image. We do this by adding noise and solving linear equations based on a local linear approximation of the learned network, without building or inverting large covariance matrices. Across super-resolution, deblurring, and inpainting on FFHQ and COCO, PASEO achieves strong perceptual quality while running up to 9x…
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arXiv cs.LGSep 24
FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference
Gatien Séguy, Thomas Rodet
Diffusion models are powerful priors for linear inverse problems, but the reference guidance methods, Diffusion Posterior Sampling (DPS) and Pseudoinverse-Guided Diffusion Models ($Π$GDM), rely on scalar hyperparameters tuned per task, usually against the ground truth. We introduce FB-GDM, a fully-Bayesian guided diffusion method that removes this calibration step. Starting from the Gaussian approximation of $Π$GDM, we derive a closed-form conditional score that depends on two precision parameters (inverse variances), one associated with the denoising approximation and one with the observation likelihood, and treat them as latent variables inferred by variational inference at each reverse step. A separable factorization makes each update scale linearly with the number of pixels, so the inference stays tractable at full image resolution, at a cost comparable to one $Π$GDM run. FB-GDM requires neither the noise level nor the ground truth: its only inputs are the observation and the forward operator. Experiments on CelebA-HQ inverse problems establish two results. (i) The precision parameters, inferred from the observation alone, allow FB-GDM to outperform $Π$GDM at its nominal…
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Results

Papers

arXiv cs.CVSep 25
PhoenixSR: Generative Heterogeneous Distillation Unleashes Efficient Models for Real-World Super-Resolution
Xin Di, Mingyu Shi, Yuanfei Bao, Long Peng, Yue Zhao +5
Real-world image super-resolution (SR) requires recovering perceptually realistic high-resolution images from complex low-resolution observations while preserving faithful content. Diffusion-based SR benefits from strong generative priors but incurs substantial computational overhead, whereas feed-forward CNN and Transformer SR models are efficient yet often struggle to recover realistic high-frequency details. This motivates a natural question: can diffusion priors be transferred to existing diffusion-free SR networks without introducing diffusion components at inference time? To this end, we propose PhoenixSR, a generative heterogeneous distillation framework that transfers diffusion priors to independently designed feed-forward SR networks through score-based distribution matching. Rather than aligning heterogeneous features or imitating sampled diffusion outputs, PhoenixSR uses the pretrained diffusion model as distribution-level supervision, while paired SR supervision preserves reconstruction fidelity. To make distribution matching effective for fidelity-sensitive SR, we introduce Heterogeneous Distribution Adaptation, which adapts the target score to the SR domain,…
PDF
arXiv cs.LGSep 28
GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priors
Wangqian Chen, Hao Wang, Yumeng Zhang, Jiajia Guo, Junting Chen +1
Active grounding of a frozen diffusion prior requires jointly determining where new measurements should be taken and how they should be used to refine the current reconstruction. Posterior-ensemble-based methods can estimate acquisition utility from generated samples, but require repeated ensemble generation as observations accumulate and capture posterior geometry only through empirical statistics. This paper proposes GPARA, which learns a context-dependent graph surrogate over diffusion prediction residuals, inducing an explicitly reusable posterior response operator that propagates measurement innovations to unobserved variables and evaluates candidate measurements through weighted posterior-risk reduction. Under the matched surrogate, we show that the same response operator also determines expected one-step acquisition benefit and yields an analytic ranking consistent with expected reconstruction improvement. A bounded learned residual calibrates the analytic utility to account for surrogate mismatch, while a small prior ensemble is generated once and reconditioned to update risk weights without repeated diffusion posterior sampling during acquisition. Experiments on two…
PDF
arXiv cs.CLOct 9
Rethinking the Roles of Diffusion and Decoding: Predictive-State Flows for Parallel Language Generation
Jinjin He, Xinsong Feng, Lucheng Fu, Sinan Wang, Bo Zhu +1
In continuous diffusion language models (DLMs), latents generated by the diffusion prior are mapped almost deterministically to tokens, either by a decoder or through a token embedding matrix. Unlike in image generation, where visual details can vary continuously, the diffusion prior must capture fine-grained discrete token choices in continuous space, which can make the joint latent distribution difficult to model. We argue that generative roles should instead be divided: the diffusion prior should generate high-level predictive information, while the decoder should resolve the remaining token-level choices. Based on this view, we introduce Predictive-State Flows (PSF), which partitions a sequence into blocks and associates each block with a predictive state computed solely from the preceding context. A rectified-flow prior generates the sequence of predictive states, after which a block-causal decoder generates all blocks in parallel, autoregressively only within each block. This design reduces diffusion from L token-level states to K << L predictive states and reduces token-level sequential depth to L/K. On unconditional OpenWebText generation, a 197M-parameter model with K=8…
PDF
arXiv stat.MLOct 7
Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
Dai Hai Nguyen, Duc Dung Nguyen
Split Gibbs sampling (SGS) is a popular framework for posterior sampling in Bayesian imaging inverse problems. It decouples a Gaussian data-fidelity term from a complex prior through an auxiliary variable, so the data variable is updated exactly and only the prior-side conditional is hard to sample. Existing samplers treat this conditional in one of two ways. Plug-and-play SGS runs a multi-step diffusion denoiser at every iteration, which is expensive and lacks non-asymptotic guarantees. Langevin-within-SGS takes cheap overdamped Langevin steps but needs many iterations. We propose RED-KLwSGS, which keeps the exact Gaussian update for the data variable and updates the auxiliary variable with underdamped (kinetic) Langevin diffusions driven by a one-shot denoising score, at the same per-iteration cost as Langevin-within-SGS. We prove non-asymptotic Wasserstein-2 convergence in continuous and discrete time for strongly log-concave priors. We also introduce Joint-RED-KLwSGS, which applies kinetic Langevin diffusions to both variables. Experiments with Denoising diffusion probabilistic models as diffusion priors on FFHQ and ImageNet datasets show faster convergence and high-quality…
PDF
arXiv cs.LGOct 7
Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps
So Takao, Gregory David Bellchambers, Luke Ye, Sanmitra Ghosh, Michalis Michaelides
Pretrained diffusion models are powerful priors for inverse problems, but posterior sampling under nonlinear, non-differentiable forward models remain hard. We introduce diffusion waltz, an MCMC method using SDEdit-style noising-denoising as a proposal, corrected via Metropolis-Hastings for exact posterior sampling without prior evaluation. We further propose injecting observations into the proposal while preserving exactness, using a gradient-free ensemble Kalman update. On a non-differentiable Navier-Stokes initial condition recovery task, diffusion waltz outperforms existing baselines across different noise and nonlinearity regimes.
PDF
arXiv eess.SPSep 24
Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
Yi Zhang, Rui Guo, Mengchu Xu, Zhaofeng Liu, Yonina C. Eldar
Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.
PDF
arXiv cs.LGOct 9
When Edge Independence Fails: Joint Graph Diffusion with Latent Sociability Priors
Adarsh Jamadandi, Nicolas Keriven, Aline Roumy
Discrete graph diffusion models corrupt graph structure through independent edge updates with a Markovian noise model. Combined with the exchangeability requirement on the output distribution, the terminal prior is necessarily an Erdős--Rényi (E-R) random graph. This has a fundamental consequence for unconditional graph generation without node features: in the large graph limit, any GNN denoiser applied to an E-R graph approximately outputs an E-R graph, making effective denoising difficult. In practice, generated graphs fail to recover meaningful node heterogeneity and higher-order structure. Previous models introduced specialized node features to compensate, framing this as an expressivity problem, while the role of the prior remained unexamined. We instead address the root cause by introducing the Latent Sociability Prior (LSP) and a join} diffusion process that co-evolves latent node sociability variables and graph structure, removing edge independence while preserving exchangeability. Unlike existing latent graph diffusion methods, the sociability mechanism requires no complex encoder: its sole role is to guide edge updates and preserve node heterogeneity throughout the…
PDF
arXiv cs.LGOct 10
Pro-t-VAE: Closed-Form Student's t Mixtures for Robust Prototype Discovery
Zhikang Xu, Jiarui Xing, Jian Wang
We present a robust deep generative framework for unsupervised image prototype discovery, built on a heavy-tailed Student's t mixture prior, that bridges statistical robustness and mathematical tractability. Existing generative approaches typically rely on noise-prone Gaussian priors or computationally intensive diffusion models; neither simultaneously provides explicit latent structure nor exact analytic optimization. While diffusion models can yield strong priors, iterative sampling and intractable likelihoods limit scalability and interpretability for prototype discovery. We address these issues by constructing a Student's t latent space via a Bayesian scale-mixture formulation. This yields a fully closed-form augmented ELBO for unsupervised Student's t mixture variational autoencoders, which, to our knowledge, is the first such objective applied to robust image prototype discovery, avoiding biased variational approximations and high computational costs in prior heavy-tailed or diffusion-based frameworks. Treating precision as a latent variable automatically modulates each data point's influence, downweighting outliers to learn a data-dependent measure of trust. The result is…
PDF
arXiv cs.ROOct 5
P3: Persistent Particle Planning for Constrained Diffusion Control
Hikmet Simsir, Mahyar Fardinfar, Ozgur S. Oguz
Diffusion models provide expressive priors over trajectories, but adapting these priors to test-time constraints requires maintaining feasibility and consistency across successive control decisions. We introduce Persistent Particle Planning (P3), a sequential Monte Carlo framework for diffusion control that maintains a weighted population of candidate plans across replanning steps. At each control step, P3 shifts and partially re-noises the candidate trajectories, refines them under the latest observation, and uses constraint-aware weighting and resampling to select among alternative continuations without retraining the diffusion model. We consider denoising and replanning as one Feynman--Kac particle system and analyze it under an idealized repair. We prove that the re-noising depth controls how reliably a kept plan stays on its route, and that keeping a rare, well-separated route takes far fewer plans than rediscovering it by sampling from scratch. Experiments under multiple test-time constraint configurations show that population reuse reduces route switching and improves success without constraint violations. Because P3 refines earlier plans instead of redrawing them, it also…
PDF
arXiv cs.ROOct 9
Akule: Fast and Scalable Multi-Robot Motion Planning via Sparse Interaction Diffusion
Manav Vora, Gokul Puthumanaillam, Aditya Penumarti, Jane Shin, Melkior Ornik
Diffusion models provide expressive trajectory priors for multi-robot motion planning (MRMP), but scaling them to large teams requires coordinating individual motions without expensive joint computation. We introduce Akule, a sparse interaction diffusion framework that augments a frozen single-robot prior with three learned modules: a reusable pairwise correction model $R_φ$, a contextual selector $U_ψ$ that determines which corrections to evaluate, and a composer $G_ω$ that combines their effects through context-dependent signed weights. This decomposition separates which interactions merit computation from how their effects should be combined into coordinated denoising updates. We train $R_φ$ using matched pairwise trajectory optimizations, then learn $G_ω$ and $U_ψ$ from physically optimized joint trajectories without requiring a prescribed ground-truth interaction graph. The resulting joint proposals are passed to a downstream search-based planner for validation and repair. Across diverse MRMP benchmarks, Akule achieves competitive planning success, complete-planner speedups of up to $25\times$, zero-shot population transfer, and successful planning with up to $256$ robots.…
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arXiv cs.CVOct 19▲ 26
RoAR-VAE: Improving Latent Diffusability through Robust Prediction
Yang Yue, Fangyun Wei, Yitong Wang, Jinjing Zhao, Henry Zheng +2
An effective visual tokenizer must preserve image fidelity while producing latents that downstream diffusion models can learn efficiently. Prior work improves latent diffusability through semantic alignment or joint tokenizer--diffusion training. Revisiting REPA-E, a representative approach, we find that removing its diffusion objective and dedicated generative blocks while retaining semantic prediction from corrupted latents yields comparable downstream generation performance under a matched setting. This observation motivates a general principle of robust prediction: generation-relevant information should remain recoverable from corrupted latents. We instantiate this principle with two complementary objectives. RobustAlign predicts pretrained semantic features from corrupted latents to preserve high-level structure, while RobustRecon reconstructs the clean image to retain fine-grained spatial and appearance information. Together, they form Robust Alignment and Reconstruction VAE (RoAR-VAE). Our analysis suggests that robust prediction improves diffusability by making useful information more accessible in high-variance latent directions, which diffusion models tend to learn…
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arXiv cs.LGOct 3
Backward-Consistent Diffusion Sampling for Sparsely Observed PDE Inverse Problems
Yida Pan, Muhammad H. Ashiq, Chanyong Jung, Yixuan Jia, Jonah M. Miller +2
Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for which generative machine learning methods (e.g., diffusion models) have become a leading way to encode the prior. Recent state-of-the-art diffusion solvers lift these priors to function spaces, finding a physics-consistent reconstruction in the output space of the diffusion denoiser. We prove that, in a discontinuous PDE setting, output space methods can result in failure to appropriately minimize the unobserved error with the correct coefficient field. Consequently, we propose Function space Backward-Consistent Sampling (FunBCS), an input space optimization approach for solving PDE problems which aims to find the best input such that the denoiser reconstruction is physics-consistent. We then prove that FunBCS appropriately minimizes the unobserved error, unlike output space optimization methods. Per our theoretical analysis, we also provide insights on how to dynamically allocate the number of input space optimization steps used throughout the sampling process. Our evaluations, across four PDE inverse problems (including the…
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arXiv cs.AISep 21
Unsupervised Brain Anomaly Detection as a Bayesian Inverse Problem with Diffusion Prior
Hugues Roy, Reuben Dorent, Ninon Burgos
Unsupervised anomaly detection (UAD) aims to localize abnormal regions in medical scans without pixel-level annotations. A typical strategy seeks to reconstruct a pseudo-healthy image that preserves subject-specific anatomy. Recently, diffusion models have been proposed to perform UAD. However, these methods rely on heuristic noise schedules or synthetic corruptions to balance subject-specificity and anomaly removal. In this work, we propose an alternative formulation of UAD as a Bayesian inverse problem under a diffusion prior. First, we introduce a latent spatial anomaly mask that models pixel-wise consistency between a test image and its latent corresponding pseudo-healthy image. Then, we propose an approximation of the unknown generation process that links healthy anatomy, anomalies, and the observed image, enabling a well-defined likelihood within the Bayesian framework. Building on recent advances in diffusion-based inverse problem methods, we jointly infer the pseudo-healthy image and the anomaly mask via annealed posterior sampling. We evaluate our approach on FDG PET (ADNI) and FLAIR MRI (BraTS 2021), demonstrating improved anomaly localization performance compared to…
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arXiv stat.MLOct 13
Structure-aware Bayesian full waveform inversion via diffusion-regularized Stein variational gradient descent
Chao Li, Mrinal K. Sen, Sergey Fomel, Yangkang Chen
Full waveform inversion (FWI) is a powerful tool for high-resolution subsurface model reconstruction, but it remains highly nonlinear and ill-posed, especially when the initial model is inaccurate or the acquired data are noisy and incomplete. Annealed Stein variational gradient descent (ASVGD) provides a particle-based Bayesian framework for FWI by approximating the posterior distribution with an ensemble of velocity models, thereby enabling uncertainty quantification beyond a single deterministic solution. However, conventional ASVGD-FWI commonly relies on simple handcrafted priors, such as Gaussian or smoothing assumptions, which are often insufficient to represent complex geological structures. To address this limitation, we introduce a learned diffusion model (DM) as an implicit regularization mechanism within the ASVGD-FWI framework. Instead of explicitly evaluating the diffusion prior density, the trained diffusion model acts as a learned geological projection operator that guides updated particles toward the distribution of plausible velocity models. In this way, the proposed method combines data consistency from FWI, posterior diversity from ASVGD, and structural realism…
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arXiv cs.CVOct 13
Recasting DiT for Extreme Image Compression with Hierarchical Visual Priors
Yunuo Chen, Jingnan Gao, Bing He, Jinjing Zhao, Chuqin Zhou +4
Pretrained diffusion models provide powerful generative priors for extreme image compression, but their stochastic, iterative generation processes are not designed to decode compressed representations directly. We present PrismCodec, which recasts a pretrained Diffusion Transformer (DiT) as a bitstream-grounded one-step generative decoder. PrismCodec uses the decoded representation in two complementary roles: a projected codec state defines the starting state for generation, while hierarchical visual priors derived from the same decoded latent provide semantic and structural guidance. To bridge the gap between stochastic, iterative generation and deterministic one-step decoding, we develop a progressive adaptation strategy. We first learn codec-conditioned transport from a noisy neighborhood centered on the codec state, distill it into a one-step mapping, and finally anneal the source perturbation to zero during end-to-end optimization. The resulting decoder reconstructs deterministically from the received representation without additional conditioning bits. Across Kodak, CLIC, and DIV2K, PrismCodec consistently improves rate-perception performance over prior generative codecs,…
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arXiv cs.LGOct 9
Spanning Diffusion and Flow-based Posterior Sampling via Exact Gaussian Conditioning
Teo Deveney, Lea Bogensperger, Hok Shing Wong
Flow-matching and diffusion models are increasingly used as priors for linear inverse problems, however, most methods are bespoke to one class of trajectory prior. Plug-and-play methods have been proposed, however these implicitly decorrelate the guided trajectory, resulting in broad priors that can struggle when data is sparse. This work proposes $β$-Flow: a general plug-and-play method indexed by a correlation parameter $β$ that generalises over flow, diffusion, and decorrelated priors, and a confidence parameter $κ$ that controls how strongly the path distribution is enforced. Each step requires only one forward evaluation of a denoising network, followed by a Gaussian conditioning step. This step is an exact Kalman update that is not dependent on network gradients. We show that many existing guided samplers can be interpreted as instances or approximations of our method, each implicitly using a different trajectory prior and operator in place of the Kalman gain. From this viewpoint, we provide a qualitative comparison of methods in terms of their implicit biases and assumptions. We demonstrate consistently state-of-the-art level performance across 7 inverse problems over 4…
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arXiv cs.CVOct 13▲ 3
H-DDCM: Hadamard Codebooks for Fast Generative Image and Video Compression
Or Ronai, Vladimir Kulikov, Tomer Michaeli
Training-free diffusion-based compression methods repurpose the generative priors of a diffusion or a flow model to compress data without retraining them as task-specific codecs. Recent codebook-based approaches such as Turbo-DDCM achieve strong perceptual quality at ultra-low bitrates, but their reliance on dense Gaussian codebooks remains costly in both memory and computation, and scales poorly with the large latent dimensions of modern image and video generators. Their combinatorial bitstream encoding further becomes computationally heavy at this scale. We introduce H-DDCM, a scalable generative compression framework that replaces Gaussian codebooks with implicit randomized Hadamard dictionaries. The fast Walsh-Hadamard transform allows for implicitly synthesizing full-dimensional dictionaries with $O(d \log d)$ compute for projection and reconstruction and $O(d)$ memory, without materializing the full-dimensional dictionary. We further introduce an efficient table-free lexicographic coding scheme that makes combinatorial encoding practical at larger dimensions. Beyond images, we adapt the framework to an autoregressive video flow model and develop a streaming compression…
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arXiv cs.CVOct 13
$\mathrm{S}^3$-PnP: Plug-and-Play Denoising for Scientific Imaging with Self-Supervised Score Priors
Yukun Cui, Jiangshe Zhang, Shuang Xu, Lilun Deng, Haowen Bai +4
Modern image restoration methods increasingly rely on large-scale supervised training, yet clean targets are often prohibitively difficult to obtain in scientific imaging modalities such as hyperspectral imaging (HSI) and magnetic resonance imaging (MRI). Plug-and-play ADMM (PnP-ADMM) with pretrained diffusion priors offers a promising alternative, but the learned prior distribution can mismatch both the target scientific image distribution and the distribution of ADMM denoiser inputs induced by dual feedback. To mitigate these mismatches, we propose $\mathrm{S}^3$-PnP, a self-supervised plug-and-play restoration framework that learns a score prior directly from observation-derived ADMM intermediate states, without clean training targets or externally pretrained weights. Specifically, the learned score corrects the input to the analytical prior update, combining observation-driven corrections with analytical regularization. We further analyze the convergence and reconstruction error of the corrected ADMM algorithm assuming an ideal score and quadratic data fidelity. Experiments on reference-guided HSI restoration, single-image HSI denoising, and MRI denoising demonstrate…
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arXiv cs.LGSep 27
Perturb-and-Solve: Efficient Learned-Operator Conditioning for Latent Diffusion Inverse Problems
Abduragim Shtanchaev, Arip Asadulaev, Luiza Labazanova, Aidar Alimbayev, Karim Salta +1
Latent diffusion models serve as powerful priors for solving inverse problems in image restoration, such as deblurring, inpainting, and super-resolution. Current methods have a trade-off between generality and efficiency. Solvers that are restricted to a fixed set of degradation operators are fast and efficient. Methods that support arbitrary degradation operators are slow and require gradients through the diffusion network. To break this bottleneck, we introduce PASEO (Perturb-And-Solve for Efficient Operator conditioning), a method that uses a small (1M parameters) learned network to degrade diffusion model predictions in latent space. PASEO supports learned degradation operators without back-propagating through the diffusion network. We efficiently sample reconstructions from an approximate posterior by combining the diffusion model's prediction with the observed image. We do this by adding noise and solving linear equations based on a local linear approximation of the learned network, without building or inverting large covariance matrices. Across super-resolution, deblurring, and inpainting on FFHQ and COCO, PASEO achieves strong perceptual quality while running up to 9x…
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arXiv cs.LGSep 24
FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference
Gatien Séguy, Thomas Rodet
Diffusion models are powerful priors for linear inverse problems, but the reference guidance methods, Diffusion Posterior Sampling (DPS) and Pseudoinverse-Guided Diffusion Models ($Π$GDM), rely on scalar hyperparameters tuned per task, usually against the ground truth. We introduce FB-GDM, a fully-Bayesian guided diffusion method that removes this calibration step. Starting from the Gaussian approximation of $Π$GDM, we derive a closed-form conditional score that depends on two precision parameters (inverse variances), one associated with the denoising approximation and one with the observation likelihood, and treat them as latent variables inferred by variational inference at each reverse step. A separable factorization makes each update scale linearly with the number of pixels, so the inference stays tractable at full image resolution, at a cost comparable to one $Π$GDM run. FB-GDM requires neither the noise level nor the ground truth: its only inputs are the observation and the forward operator. Experiments on CelebA-HQ inverse problems establish two results. (i) The precision parameters, inferred from the observation alone, allow FB-GDM to outperform $Π$GDM at its nominal…
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