arXiv subjects

Peyman Milanfar

Publications and source records attributed to Peyman Milanfar.

At least 19 recordsLinked to original sources

arXiv2026

A Lagrangian View of Flow Matching

Modern explicit-time generative models, such as Flow Matching [Lipman et al., 2023] and Rectified Flow [Liu et al., 2023], are typically derived top-down via Optimal Transport and the continuity equation. This standard Eulerian approach focuses on the macroscopic transport of probability mass. In this paper, we present an alternative, bottom-up mechanical derivation grounded in a Lagrangian (particle-centric) perspective. By analyzing the local Taylor expansion of a continuous denoiser, we motivate a strict invariance condition required for optimal, singlestep generation: the conservation of target identity. Enforcing this condition yields a governing quasi-linear advection Partial Differential Equation (PDE). We demonstrate that solving this PDE via the Method of Characteristics analytically yields the straight-line trajectories of Flow Matching. This geometric perspective isolates the Jacobian of the denoiser as the primary source of trajectory curvature, providing a direct mathematical explanation for why straight-line flows enable massive step sizes, and why empirical models require distillation to flatten intersecting characteristics.

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arXiv2026

The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning

Autonomous (noise-agnostic) generative models, such as Equilibrium Matching and blind diffusion, challenge the standard paradigm by learning a single, time-invariant vector field that operates without explicit noise-level conditioning. While recent work suggests that high-dimensional concentration allows these models to implicitly estimate noise levels from corrupted observations, a fundamental paradox remains: what is the underlying landscape being optimized when the noise level is treated as a random variable, and how can a bounded, noise-agnostic network remain stable near the data manifold where gradients typically diverge? We resolve this paradox by formalizing Marginal Energy, $E_{\text{marg}}(\mathbf{u}) = -\log p(\mathbf{u})$, where $p(\mathbf{u}) = \int p(\mathbf{u}|t)p(t)dt$ is the marginal density of the noisy data integrated over a prior distribution of unknown noise levels. We prove that generation using autonomous models is not merely blind denoising, but a specific form of Riemannian gradient flow on this Marginal Energy. Through a novel relative energy decomposition, we demonstrate that while the raw Marginal Energy landscape possesses a $1/t^p$ singularity normal to the data manifold, the learned time-invariant field implicitly incorporates a local conformal metric that perfectly counteracts the geometric singularity, converting an infinitely deep potential well into a stable attractor. We also establish the structural stability conditions for sampling with autonomous models. We identify a ``Jensen Gap'' in noise-prediction parameterizations that acts as a high-gain amplifier for estimation errors, explaining the catastrophic failure observed in deterministic blind models. Conversely, we prove that velocity-based parameterizations are inherently stable because they satisfy a bounded-gain condition that absorbs posterior uncertainty into a smooth geometric drift.

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arXiv2025

Generative Manifold Distillation: Aligning Restoration Trajectories with Natural Image Prior

Pre-trained image restoration models often fail on out-of-distribution (OOD) real-world degradations. Adapting to these domains is challenging as real-world data lacks paired ground truth, and unsupervised methods often require unstable architectural changes. We propose Generative Manifold Distillation (GMD), which reframes domain adaptation as geometric manifold alignment. GMD operates in a strictly unpaired setting, requiring only low-quality (LQ) target observations. By leveraging the flow-matching dynamics of a frozen text-to-image foundation model, GMD projects off-manifold restorations onto the natural image manifold to generate high-quality pseudo-targets. To ensure stability, a quality-gated manifold filter rejects off-manifold samples, while source-anchored trajectory regularization prevents error accumulation. Ultimately, GMD distills a powerful generative prior into an efficient restoration network. Experiments demonstrate that GMD seamlessly adapts to new distributions using only LQ inputs, drastically improving perceptual quality with zero architectural modifications or added inference latency.

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arXiv2025

Kernel Density Steering: Inference-Time Scaling via Mode Seeking for Image Restoration

Diffusion models show promise for image restoration, but existing methods often struggle with inconsistent fidelity and undesirable artifacts. To address this, we introduce Kernel Density Steering (KDS), a novel inference-time framework promoting robust, high-fidelity outputs through explicit local mode-seeking. KDS employs an $N$-particle ensemble of diffusion samples, computing patch-wise kernel density estimation gradients from their collective outputs. These gradients steer patches in each particle towards shared, higher-density regions identified within the ensemble. This collective local mode-seeking mechanism, acting as "collective wisdom", steers samples away from spurious modes prone to artifacts, arising from independent sampling or model imperfections, and towards more robust, high-fidelity structures. This allows us to obtain better quality samples at the expense of higher compute by simultaneously sampling multiple particles. As a plug-and-play framework, KDS requires no retraining or external verifiers, seamlessly integrating with various diffusion samplers. Extensive numerical validations demonstrate KDS substantially improves both quantitative and qualitative performance on challenging real-world super-resolution and image inpainting tasks.

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arXiv2025

UniRes: Universal Image Restoration for Complex Degradations

Real-world image restoration is hampered by diverse degradations stemming from varying capture conditions, capture devices and post-processing pipelines. Existing works make improvements through simulating those degradations and leveraging image generative priors, however generalization to in-the-wild data remains an unresolved problem. In this paper, we focus on complex degradations, i.e., arbitrary mixtures of multiple types of known degradations, which is frequently seen in the wild. A simple yet flexible diffusionbased framework, named UniRes, is proposed to address such degradations in an end-to-end manner. It combines several specialized models during the diffusion sampling steps, hence transferring the knowledge from several well-isolated restoration tasks to the restoration of complex in-the-wild degradations. This only requires well-isolated training data for several degradation types. The framework is flexible as extensions can be added through a unified formulation, and the fidelity-quality trade-off can be adjusted through a new paradigm. Our proposed method is evaluated on both complex-degradation and single-degradation image restoration datasets. Extensive qualitative and quantitative experimental results show consistent performance gain especially for images with complex degradations.

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arXiv2025

TextSR: Diffusion Super-Resolution with Multilingual OCR Guidance

While recent advancements in Image Super-Resolution (SR) using diffusion models have shown promise in improving overall image quality, their application to scene text images has revealed limitations. These models often struggle with accurate text region localization and fail to effectively model image and multilingual character-to-shape priors. This leads to inconsistencies, the generation of hallucinated textures, and a decrease in the perceived quality of the super-resolved text. To address these issues, we introduce TextSR, a multimodal diffusion model specifically designed for Multilingual Scene Text Image Super-Resolution. TextSR leverages a text detector to pinpoint text regions within an image and then employs Optical Character Recognition (OCR) to extract multilingual text from these areas. The extracted text characters are then transformed into visual shapes using a UTF-8 based text encoder and cross-attention. Recognizing that OCR may sometimes produce inaccurate results in real-world scenarios, we have developed two innovative methods to enhance the robustness of our model. By integrating text character priors with the low-resolution text images, our model effectively guides the super-resolution process, enhancing fine details within the text and improving overall legibility. The superior performance of our model on both the TextZoom and TextVQA datasets sets a new benchmark for STISR, underscoring the efficacy of our approach.

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arXiv2025

Reference-Guided Identity Preserving Face Restoration

Preserving face identity is a critical yet persistent challenge in diffusion-based image restoration. While reference faces offer a path forward, existing reference-based methods often fail to fully exploit their potential. This paper introduces a novel approach that maximizes reference face utility for improved face restoration and identity preservation. Our method makes three key contributions: 1) Composite Context, a comprehensive representation that fuses multi-level (high- and low-level) information from the reference face, offering richer guidance than prior singular representations. 2) Hard Example Identity Loss, a novel loss function that leverages the reference face to address the identity learning inefficiencies found in the existing identity loss. 3) A training-free method to adapt the model to multi-reference inputs during inference. The proposed method demonstrably restores high-quality faces and achieves state-of-the-art identity preserving restoration on benchmarks such as FFHQ-Ref and CelebA-Ref-Test, consistently outperforming previous work.

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arXiv2025

The Power of Context: How Multimodality Improves Image Super-Resolution

Single-image super-resolution (SISR) remains challenging due to the inherent difficulty of recovering fine-grained details and preserving perceptual quality from low-resolution inputs. Existing methods often rely on limited image priors, leading to suboptimal results. We propose a novel approach that leverages the rich contextual information available in multiple modalities -- including depth, segmentation, edges, and text prompts -- to learn a powerful generative prior for SISR within a diffusion model framework. We introduce a flexible network architecture that effectively fuses multimodal information, accommodating an arbitrary number of input modalities without requiring significant modifications to the diffusion process. Crucially, we mitigate hallucinations, often introduced by text prompts, by using spatial information from other modalities to guide regional text-based conditioning. Each modality's guidance strength can also be controlled independently, allowing steering outputs toward different directions, such as increasing bokeh through depth or adjusting object prominence via segmentation. Extensive experiments demonstrate that our model surpasses state-of-the-art generative SISR methods, achieving superior visual quality and fidelity. See project page at https://mmsr.kfmei.com/.

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arXiv2024

On the Relation Between Linear Diffusion and Power Iteration

Recently, diffusion models have gained popularity due to their impressive generative abilities. These models learn the implicit distribution given by the training dataset, and sample new data by transforming random noise through the reverse process, which can be thought of as gradual denoising. In this work, we examine the generation process as a ``correlation machine'', where random noise is repeatedly enhanced in correlation with the implicit given distribution. To this end, we explore the linear case, where the optimal denoiser in the MSE sense is known to be the PCA projection. This enables us to connect the theory of diffusion models to the spiked covariance model, where the dependence of the denoiser on the noise level and the amount of training data can be expressed analytically, in the rank-1 case. In a series of numerical experiments, we extend this result to general low rank data, and show that low frequencies emerge earlier in the generation process, where the denoising basis vectors are more aligned to the true data with a rate depending on their eigenvalues. This model allows us to show that the linear diffusion model converges in mean to the leading eigenvector of the underlying data, similarly to the prevalent power iteration method. Finally, we empirically demonstrate the applicability of our findings beyond the linear case, in the Jacobians of a deep, non-linear denoiser, used in general image generation tasks.

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arXiv2024

Stochastic Deep Restoration Priors for Imaging Inverse Problems

Deep neural networks trained as image denoisers are widely used as priors for solving imaging inverse problems. While Gaussian denoising is thought sufficient for learning image priors, we show that priors from deep models pre-trained as more general restoration operators can perform better. We introduce Stochastic deep Restoration Priors (ShaRP), a novel method that leverages an ensemble of such restoration models to regularize inverse problems. ShaRP improves upon methods using Gaussian denoiser priors by better handling structured artifacts and enabling self-supervised training even without fully sampled data. We prove ShaRP minimizes an objective function involving a regularizer derived from the score functions of minimum mean square error (MMSE) restoration operators, and theoretically analyze its convergence. Empirically, ShaRP achieves state-of-the-art performance on tasks such as magnetic resonance imaging reconstruction and single-image super-resolution, surpassing both denoiser-and diffusion-model-based methods without requiring retraining.

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arXiv2024

A Survey on Diffusion Models for Inverse Problems

Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and reconstruction, by treating diffusion models as unsupervised priors. This survey provides a comprehensive overview of methods that utilize pre-trained diffusion models to solve inverse problems without requiring further training. We introduce taxonomies to categorize these methods based on both the problems they address and the techniques they employ. We analyze the connections between different approaches, offering insights into their practical implementation and highlighting important considerations. We further discuss specific challenges and potential solutions associated with using latent diffusion models for inverse problems. This work aims to be a valuable resource for those interested in learning about the intersection of diffusion models and inverse problems.

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arXiv2024

Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learning

Denoising, the process of reducing random fluctuations in a signal to emphasize essential patterns, has been a fundamental problem of interest since the dawn of modern scientific inquiry. Recent denoising techniques, particularly in imaging, have achieved remarkable success, nearing theoretical limits by some measures. Yet, despite tens of thousands of research papers, the wide-ranging applications of denoising beyond noise removal have not been fully recognized. This is partly due to the vast and diverse literature, making a clear overview challenging. This paper aims to address this gap. We present a clarifying perspective on denoisers, their structure, and desired properties. We emphasize the increasing importance of denoising and showcase its evolution into an essential building block for complex tasks in imaging, inverse problems, and machine learning. Despite its long history, the community continues to uncover unexpected and groundbreaking uses for denoising, further solidifying its place as a cornerstone of scientific and engineering practice.

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arXiv2024

ArtVLM: Attribute Recognition Through Vision-Based Prefix Language Modeling

Recognizing and disentangling visual attributes from objects is a foundation to many computer vision applications. While large vision language representations like CLIP had largely resolved the task of zero-shot object recognition, zero-shot visual attribute recognition remains a challenge because CLIP's contrastively-learned vision-language representation cannot effectively capture object-attribute dependencies. In this paper, we target this weakness and propose a sentence generation-based retrieval formulation for attribute recognition that is novel in 1) explicitly modeling a to-be-measured and retrieved object-attribute relation as a conditional probability graph, which converts the recognition problem into a dependency-sensitive language-modeling problem, and 2) applying a large pretrained Vision-Language Model (VLM) on this reformulation and naturally distilling its knowledge of image-object-attribute relations to use towards attribute recognition. Specifically, for each attribute to be recognized on an image, we measure the visual-conditioned probability of generating a short sentence encoding the attribute's relation to objects on the image. Unlike contrastive retrieval, which measures likelihood by globally aligning elements of the sentence to the image, generative retrieval is sensitive to the order and dependency of objects and attributes in the sentence. We demonstrate through experiments that generative retrieval consistently outperforms contrastive retrieval on two visual reasoning datasets, Visual Attribute in the Wild (VAW), and our newly-proposed Visual Genome Attribute Ranking (VGARank).

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arXiv2024

SPIRE: Semantic Prompt-Driven Image Restoration

Text-driven diffusion models have become increasingly popular for various image editing tasks, including inpainting, stylization, and object replacement. However, it still remains an open research problem to adopt this language-vision paradigm for more fine-level image processing tasks, such as denoising, super-resolution, deblurring, and compression artifact removal. In this paper, we develop SPIRE, a Semantic and restoration Prompt-driven Image Restoration framework that leverages natural language as a user-friendly interface to control the image restoration process. We consider the capacity of prompt information in two dimensions. First, we use content-related prompts to enhance the semantic alignment, effectively alleviating identity ambiguity in the restoration outcomes. Second, our approach is the first framework that supports fine-level instruction through language-based quantitative specification of the restoration strength, without the need for explicit task-specific design. In addition, we introduce a novel fusion mechanism that augments the existing ControlNet architecture by learning to rescale the generative prior, thereby achieving better restoration fidelity. Our extensive experiments demonstrate the superior restoration performance of SPIRE compared to the state of the arts, alongside offering the flexibility of text-based control over the restoration effects.

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arXiv2024

Bigger is not Always Better: Scaling Properties of Latent Diffusion Models

We study the scaling properties of latent diffusion models (LDMs) with an emphasis on their sampling efficiency. While improved network architecture and inference algorithms have shown to effectively boost sampling efficiency of diffusion models, the role of model size -- a critical determinant of sampling efficiency -- has not been thoroughly examined. Through empirical analysis of established text-to-image diffusion models, we conduct an in-depth investigation into how model size influences sampling efficiency across varying sampling steps. Our findings unveil a surprising trend: when operating under a given inference budget, smaller models frequently outperform their larger equivalents in generating high-quality results. Moreover, we extend our study to demonstrate the generalizability of the these findings by applying various diffusion samplers, exploring diverse downstream tasks, evaluating post-distilled models, as well as comparing performance relative to training compute. These findings open up new pathways for the development of LDM scaling strategies which can be employed to enhance generative capabilities within limited inference budgets.

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arXiv2024

CoDi: Conditional Diffusion Distillation for Higher-Fidelity and Faster Image Generation

Large generative diffusion models have revolutionized text-to-image generation and offer immense potential for conditional generation tasks such as image enhancement, restoration, editing, and compositing. However, their widespread adoption is hindered by the high computational cost, which limits their real-time application. To address this challenge, we introduce a novel method dubbed CoDi, that adapts a pre-trained latent diffusion model to accept additional image conditioning inputs while significantly reducing the sampling steps required to achieve high-quality results. Our method can leverage architectures such as ControlNet to incorporate conditioning inputs without compromising the model's prior knowledge gained during large scale pre-training. Additionally, a conditional consistency loss enforces consistent predictions across diffusion steps, effectively compelling the model to generate high-quality images with conditions in a few steps. Our conditional-task learning and distillation approach outperforms previous distillation methods, achieving a new state-of-the-art in producing high-quality images with very few steps (e.g., 1-4) across multiple tasks, including super-resolution, text-guided image editing, and depth-to-image generation.

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arXiv2024

Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration

Inversion by Direct Iteration (InDI) is a new formulation for supervised image restoration that avoids the so-called "regression to the mean" effect and produces more realistic and detailed images than existing regression-based methods. It does this by gradually improving image quality in small steps, similar to generative denoising diffusion models. Image restoration is an ill-posed problem where multiple high-quality images are plausible reconstructions of a given low-quality input. Therefore, the outcome of a single step regression model is typically an aggregate of all possible explanations, therefore lacking details and realism. The main advantage of InDI is that it does not try to predict the clean target image in a single step but instead gradually improves the image in small steps, resulting in better perceptual quality. While generative denoising diffusion models also work in small steps, our formulation is distinct in that it does not require knowledge of any analytic form of the degradation process. Instead, we directly learn an iterative restoration process from low-quality and high-quality paired examples. InDI can be applied to virtually any image degradation, given paired training data. In conditional denoising diffusion image restoration the denoising network generates the restored image by repeatedly denoising an initial image of pure noise, conditioned on the degraded input. Contrary to conditional denoising formulations, InDI directly proceeds by iteratively restoring the input low-quality image, producing high-quality results on a variety of image restoration tasks, including motion and out-of-focus deblurring, super-resolution, compression artifact removal, and denoising.

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arXiv2023

Multiscale Structure Guided Diffusion for Image Deblurring

Diffusion Probabilistic Models (DPMs) have recently been employed for image deblurring, formulated as an image-conditioned generation process that maps Gaussian noise to the high-quality image, conditioned on the blurry input. Image-conditioned DPMs (icDPMs) have shown more realistic results than regression-based methods when trained on pairwise in-domain data. However, their robustness in restoring images is unclear when presented with out-of-domain images as they do not impose specific degradation models or intermediate constraints. To this end, we introduce a simple yet effective multiscale structure guidance as an implicit bias that informs the icDPM about the coarse structure of the sharp image at the intermediate layers. This guided formulation leads to a significant improvement of the deblurring results, particularly on unseen domain. The guidance is extracted from the latent space of a regression network trained to predict the clean-sharp target at multiple lower resolutions, thus maintaining the most salient sharp structures. With both the blurry input and multiscale guidance, the icDPM model can better understand the blur and recover the clean image. We evaluate a single-dataset trained model on diverse datasets and demonstrate more robust deblurring results with fewer artifacts on unseen data. Our method outperforms existing baselines, achieving state-of-the-art perceptual quality while keeping competitive distortion metrics.

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