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Deep Learning · Generative Models and Autoencoders

Shuangqi Li, Hieu Le, Jingyi Xu, Mathieu Salzmann

Text-to-image diffusion models have demonstrated remarkable capability in generating realistic images from arbitrary text prompts. However, they often produce inconsistent results for compositional prompts such as "two dogs" or "a penguin on the right of a bowl". Understanding these inconsistencies is crucial for reliable image generation. In this paper, we highlight the significant role of initial noise in these inconsistencies, where certain noise patterns are more reliable for compositional prompts than others. Our analyses reveal that different initial random seeds tend to guide the model to place objects in distinct image areas, potentially adhering to specific patterns of camera angles and image composition associated with the seed. To improve the model's compositional ability, we propose a method for mining these reliable cases, resulting in a curated training set of generated images without requiring any manual annotation. By fine-tuning text-to-image models on these generated images, we significantly enhance their compositional capabilities. For numerical composition, we observe relative increases of 29.3\% and 19.5\% for Stable Diffusion and PixArt-$\alpha$, respectively. Spatial composition sees even larger gains, with 60.7\% for Stable Diffusion and 21.1\% for PixArt-$\alpha$.

Deep Learning · Generative Models and Autoencoders

Yongxing Zhang, Donglin Yang, Renjie Liao

The group of permutations $S_n$, also known as the finite symmetric groups, are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over $S_n$ poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce *SymmetricDiffusers*, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over $S_n$ by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performance on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at <https://github.com/DSL-Lab/SymmetricDiffusers>.

Theory · Learning Theory

Yuchen Liang, Peizhong Ju, Yingbin Liang, Ness Shroff

The denoising diffusion model has recently emerged as a powerful generative technique, capable of transforming noise into meaningful data. While theoretical convergence guarantees for diffusion models are well established when the target distribution aligns with the training distribution, practical scenarios often present mismatches. One common case is in the zero-shot conditional diffusion sampling, where the target conditional distribution is different from the (unconditional) training distribution. These score-mismatched diffusion models remain largely unexplored from a theoretical perspective. In this paper, we present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers, focusing on target distributions with finite second moments. We show that score mismatches result in an asymptotic distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions. This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise. Interestingly, the derived convergence upper bound offers useful guidance for designing a novel bias-optimal zero-shot sampler in linear conditional models that minimizes the asymptotic bias. For such bias-optimal samplers, we further establish convergence guarantees with explicit dependencies on dimension and conditioning, applied to several interesting target distributions, including those with bounded support and Gaussian mixtures. Our findings are supported by numerical studies.

Theory · Learning Theory

Yuchen Liang, Peizhong Ju, Yingbin Liang, Ness Shroff

Accelerated diffusion models hold the potential to significantly enhance the efficiency of standard diffusion processes. Theoretically, these models have been shown to achieve faster convergence rates than the standard $\mathcal O(1/\epsilon^2)$ rate of vanilla diffusion models, where $\epsilon$ denotes the target accuracy. However, current theoretical studies have established the acceleration advantage only for restrictive target distribution classes, such as those with smoothness conditions imposed along the entire sampling path or with bounded support. In this work, we significantly broaden the target distribution classes with a new accelerated stochastic DDPM sampler. In particular, we show that it achieves accelerated performance for three broad distribution classes not considered before. Our first class relies on the smoothness condition posed only to the target density $q_0$, which is far more relaxed than the existing smoothness conditions posed to all $q_t$ along the entire sampling path. Our second class requires only a finite second moment condition, allowing for a much wider class of target distributions than the existing finite-support condition. Our third class is Gaussian mixture, for which our result establishes the first acceleration guarantee. Moreover, among accelerated DDPM type samplers, our results specialized for bounded-support distributions show an improved dependency on the data dimension $d$. Our analysis introduces a novel technique for establishing performance guarantees via constructing a tilting factor representation of the convergence error and utilizing Tweedie's formula to handle Taylor expansion terms. This new analytical framework may be of independent interest.

Deep Learning · Generative Models and Autoencoders

Hongkun Dou, Zeyu Li, Jinyang Du, Lijun Yang, Wen Yao, Yue Deng

Diffusion models, recognized for their effectiveness as generative priors, have become essential tools for addressing a wide range of visual challenges. Recently, there has been a surge of interest in leveraging Denoising processes for Regularization (DR) to solve inverse problems. However, existing methods often face issues such as mode collapse, which results in excessive smoothing and diminished diversity. In this study, we perform a comprehensive analysis to pinpoint the root causes of gradient inaccuracies inherent in DR. Drawing on insights from diffusion model distillation, we propose a novel approach called Consistency Regularization (CR), which provides stabilized gradients without the need for ODE simulations. Building on this, we introduce Hybrid Regularization (HR), a unified framework that combines the strengths of both DR and CR, harnessing their synergistic potential. Our approach proves to be effective across a broad spectrum of inverse problems, encompassing both linear and nonlinear scenarios, as well as various measurement noise statistics. Experimental evaluations on benchmark datasets, including FFHQ and ImageNet, demonstrate that our proposed framework not only achieves highly competitive results compared to state-of-the-art methods but also offers significant reductions in wall-clock time and memory consumption.

Applications · Physics

Zeyu Li, Hongkun Dou, Shen Fang, Wang Han, Yue Deng, Lijun Yang

The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in extracting features from data. However, except for the low accuracy on complex physical systems, these models often fail to comply with essential physical constraints, such as governing equations and boundary conditions. To overcome this limitation, we introduce a novel data-driven field reconstruction framework, termed the Physics-aligned Schr\"{o}dinger Bridge (PalSB). This framework leverages a diffusion bridge mechanism that is specifically tailored to align with physical constraints. The PalSB approach incorporates a dual-stage training process designed to address both local reconstruction mapping and global physical principles. Additionally, a boundary-aware sampling technique is implemented to ensure adherence to physical boundary conditions. We demonstrate the effectiveness of PalSB through its application to three complex nonlinear systems: cylinder flow from Particle Image Velocimetry experiments, two-dimensional turbulence, and a reaction-diffusion system. The results reveal that PalSB not only achieves higher accuracy but also exhibits enhanced compliance with physical constraints compared to existing methods. This highlights PalSB's capability to generate high-quality representations of intricate physical interactions, showcasing its potential for advancing field reconstruction techniques. The source code can be found at https://github.com/lzy12301/PalSB.

Applications · Everything Else

Jianwen Jiang, Chao Liang, Jiaqi Yang, Gaojie Lin, Tianyun Zhong, Yanbo Zheng

With the introduction of video diffusion model, audio-conditioned human video generation has recently achieved significant breakthroughs in both the naturalness of motion and the synthesis of portrait details. Due to the limited control of audio signals in driving human motion, existing methods often add auxiliary spatial signals such as movement regions to stabilize movements, which compromise the naturalness and freedom of motion. To address this issue, we propose an end-to-end audio-only conditioned video diffusion model named Loopy. Specifically, we designed two key modules: an inter- and intra-clip temporal module and an audio-to-latents module. These enable the model to better utilize long-term motion dependencies and establish a stronger audio-portrait movement correlation. Consequently, the model can generate more natural and stable portrait videos with subtle facial expressions, without the need for manually setting movement constraints. Extensive experiments show that Loopy outperforms recent audio-driven portrait diffusion models, delivering more lifelike and high-quality results across various scenarios. Video samples are available at https://loopyavataranony.github.io/

Applications · Computer Vision

Jianwen Jiang, Chao Liang, Jiaqi Yang, Gaojie Lin, Tianyun Zhong, Yanbo Zheng

With the introduction of video diffusion model, audio-conditioned human video generation has recently achieved significant breakthroughs in both the naturalness of motion and the synthesis of portrait details. Due to the limited control of audio signals in driving human motion, existing methods often add auxiliary spatial signals such as movement regions to stabilize movements, which compromise the naturalness and freedom of motion. To address this issue, we propose an end-to-end audio-only conditioned video diffusion model named Loopy. Specifically, we designed two key modules: an inter- and intra-clip temporal module and an audio-to-latents module. These enable the model to better utilize long-term motion dependencies and establish a stronger audio-portrait movement correlation. Consequently, the model can generate more natural and stable portrait videos with subtle facial expressions, without the need for manually setting movement constraints. Extensive experiments show that Loopy outperforms recent audio-driven portrait diffusion models, delivering more lifelike and high-quality results across various scenarios. Video samples are available at https://loopyavataranony.github.io/

Yuchen Yuchen, Xiangzhong Fang, Hanting Chen, Yunhe Wang

Sampling from diffusion models can be seen as solving the corresponding probability flow ordinary differential equation (ODE). The solving process requires a significant number of function evaluations (NFE), making it time-consuming. Recently, several solver search frameworks have attempted to find better-performing model-specific solvers. However, predicting the impact of intermediate solving strategies on final sample quality remains challenging, rendering the search process inefficient. In this paper, we propose a novel method for designing solving strategies. We first introduce a unified prediction formula for linear multistep solvers. Subsequently, we present a solver distillation framework, which enables a student solver to mimic the sampling trajectory generated by a teacher solver with more steps. We utilize the mean Euclidean distance between the student and teacher sampling trajectories as a metric, facilitating rapid adjustment and optimization of intermediate solving strategies. The design space of our framework encompasses multiple aspects, including prediction coefficients, time step schedules, and time scaling factors. Our framework has the ability to complete a solver search for Stable-Diffusion in under 12 total GPU hours. Compared to previous reinforcement learning-based search frameworks, our approach achieves over a 10$\times$ increase in search efficiency. With just 5 NFE, we achieve FID scores of 3.23 on CIFAR10, 7.16 on ImageNet-64, 5.44 on LSUN-Bedroom, and 12.52 on MS-COCO, resulting in a 2$\times$ sampling acceleration ratio compared to handcrafted solvers.

Deep Learning · Generative Models and Autoencoders

Jincheng Zhong, XiangCheng Zhang, Jianmin Wang, Mingsheng Long

Recent advancements in diffusion models have revolutionized generative modeling. However, the impressive and vivid outputs they produce often come at the cost of significant model scaling and increased computational demands. Consequently, building personalized diffusion models based on off-the-shelf models has emerged as an appealing alternative. In this paper, we introduce a novel perspective on conditional generation for transferring a pre-trained model. From this viewpoint, we propose *Domain Guidance*, a straightforward transfer approach that leverages pre-trained knowledge to guide the sampling process toward the target domain. Domain Guidance shares a formulation similar to advanced classifier-free guidance, facilitating better domain alignment and higher-quality generations. We provide both empirical and theoretical analyses of the mechanisms behind Domain Guidance. Our experimental results demonstrate its substantial effectiveness across various transfer benchmarks, achieving over a 19.6\% improvement in FID and a 23.4\% improvement in FD$_\text{DINOv2}$ compared to standard fine-tuning. Notably, existing fine-tuned models can seamlessly integrate Domain Guidance to leverage these benefits, without additional training.

Applications · Time Series

Qi Li, Zhenyu Zhang, Lei Yao, Zhaoxia Li, Tianyi Zhong, Yong Zhang

Diffusion-based denoising models have demonstrated impressive performance in probabilistic forecasting for multivariate time series (MTS). Nonetheless, existing approaches often model the entire data distribution, neglecting the variability in uncertainty across different components of the time series. This paper introduces a Diffusion-based Decoupled Deterministic and Uncertain ($\mathrm{D^3U}$) framework for probabilistic MTS forecasting. The framework integrates non-probabilistic forecasting with conditional diffusion generation, enabling both accurate point predictions and probabilistic forecasting. $\mathrm{D^3U}$ utilizes a point forecasting model to non-probabilistically model high-certainty components in the time series, generating embedded representations that are conditionally injected into a diffusion model. To better model high-uncertainty components, a patch-based denoising network (PatchDN) is designed in the conditional diffusion model. Designed as a plug-and-play framework, $\mathrm{D^3U}$ can be seamlessly integrated into existing point forecasting models to provide probabilistic forecasting capabilities. It can also be applied to other conditional diffusion methods that incorporate point forecasting models. Experiments on six real-world datasets demonstrate that our method achieves over a 20\% improvement in both point and probabilistic forecasting performance in MTS long-term forecasting compared to state-of-the-art (SOTA) probabilistic forecasting methods. Additionally, extensive ablation studies further validate the effectiveness of the $\mathrm{D^3U}$ framework.

Reinforcement Learning · Inverse

Runzhe Wu, Yiding Chen, Gokul Swamy, Kianté Brantley, Wen Sun

Adversarial Imitation Learning is traditionally framed as a two-player zero-sum game between a learner and an adversarially chosen cost function, and can therefore be thought of as the sequential generalization of a Generative Adversarial Network (GAN). However, in recent years, diffusion models have emerged as a non-adversarial alternative to GANs that merely require training a score function via regression, yet produce generations of higher quality. In response, we investigate how to lift insights from diffusion modeling to the sequential setting. We propose diffusing states and performing *score-matching* along diffused states to measure the discrepancy between the expert's and learner's states. Thus, our approach only requires training score functions to predict noises via standard regression, making it significantly easier and more stable to train than adversarial methods. Theoretically, we prove first- and second-order instance-dependent bounds with linear scaling in the horizon, proving that our approach avoids the compounding errors that stymie offline approaches to imitation learning. Empirically, we show our approach outperforms both GAN-style imitation learning baselines and discriminator-free imitation learning baselines across various continuous control problems, including complex tasks like controlling humanoids to walk, sit, crawl, and navigate through obstacles.

Deep Learning · Generative Models and Autoencoders

Tariq Berrada, Pietro Astolfi, Melissa Hall, Marton Havasi, Yohann Benchetrit, Adriana Romero-Soriano, Karteek Alahari, Michal Drozdzal, Jakob Verbeek

Latent diffusion models (LDMs) power state-of-the-art high-resolution generative image models. LDMs learn the data distribution in the latent space of an autoencoder (AE) and produce images by mapping the generated latents into RGB image space using the AE decoder. While this approach allows for efficient model training and sampling, it induces a disconnect between the training of the diffusion model and the decoder, resulting in a loss of detail in the generated images. To remediate this disconnect, we propose to leverage the internal features of the decoder to define a latent perceptual loss (LPL). This loss encourages the models to create sharper and more realistic images. Our loss can be seamlessly integrated with common autoencoders used in latent diffusion models, and can be applied to different generative modeling paradigms such as DDPM with epsilon and velocity prediction, as well as flow matching. Extensive experiments with models trained on three datasets at 256 and 512 resolution show improved quantitative -- with boosts between 6% and 20% in FID -- and qualitative results when using our perceptual loss.

Deep Learning · Generative Models and Autoencoders

Hayk Manukyan, Andranik Sargsyan, Barsegh Atanyan, Zhangyang Wang, Shant Navasardyan, Humphrey Shi

Recent progress in text-guided image inpainting, based on the unprecedented success of text-to-image diffusion models, has led to exceptionally realistic and visually plausible results. However, there is still significant potential for improvement in current text-to-image inpainting models, particularly in better aligning the inpainted area with user prompts. Therefore, we introduce $\textit{HD-Painter}$, a $\textbf{training-free}$ approach that $\textbf{accurately follows prompts}$. To this end, we design the $\textit{Prompt-Aware Introverted Attention (PAIntA)}$ layer enhancing self-attention scores by prompt information resulting in better text aligned generations. To further improve the prompt coherence we introduce the $\textit{Reweighting Attention Score Guidance (RASG)}$ mechanism seamlessly integrating a post-hoc sampling strategy into the general form of DDIM to prevent out-of-distribution latent shifts. Our experiments demonstrate that HD-Painter surpasses existing state-of-the-art approaches quantitatively and qualitatively across multiple metrics and a user study. Code is publicly available at: [https://github.com/Picsart-AI-Research/HD-Painter](https://github.com/Picsart-AI-Research/HD-Painter)

William Wang, Jiachen Li, Weixi Feng, Wenhu Chen

Latent Consistency Distillation (LCD) has emerged as a promising paradigm for efficient text-to-image synthesis. By distilling a latent consistency model (LCM) from a pre-trained teacher latent diffusion model (LDM), LCD facilitates the generation of high-fidelity images within merely 2 to 4 inference steps. However, the LCM's efficient inference is obtained at the cost of the sample quality. In this paper, we propose compensating the quality loss by aligning LCM's output with human preference during training. Specifically, we introduce Reward Guided LCD (RG-LCD), which integrates feedback from a reward model (RM) into the LCD process by augmenting the original LCD loss with the objective of maximizing the reward associated with LCM's single-step generation. As validated through human evaluation, when trained with the feedback of a good RM, the 2-step generations from our RG-LCM are favored by humans over the 50-step DDIM samples from the teacher LDM, representing a 25-time inference acceleration without quality loss. As directly optimizing towards differentiable RMs can suffer from over-optimization, we take the initial step to overcome this difficulty by proposing the use of a latent proxy RM (LRM). This novel component serves as an intermediary, connecting our LCM with the RM. Empirically, we demonstrate that incorporating the LRM into our RG-LCD successfully avoids high-frequency noise in the generated images, contributing to both improved Fréchet Inception Distance (FID) on MS-COCO and a higher HPSv2.1 score on HPSv2's test set, surpassing those achieved by the baseline LCM. Project Page: https://rg-lcd.github.io/

Deep Learning · Generative Models and Autoencoders

Yumeng Li, William H Beluch, Margret Keuper, Dan Zhang, Anna Khoreva

Despite tremendous progress in the field of text-to-video (T2V) synthesis, open-sourced T2V diffusion models struggle to generate longer videos with dynamically varying and evolving content. They tend to synthesize quasi-static videos, ignoring the necessary visual change-over-time implied in the text prompt. Meanwhile, scaling these models to enable longer, more dynamic video synthesis often remains computationally intractable. To tackle this challenge, we introduce the concept of Generative Temporal Nursing (GTN), where we adjust the generative process on the fly during inference to improve control over the temporal dynamics and enable generation of longer videos. We propose a method for GTN, dubbed VSTAR, which consists of two key ingredients: Video Synopsis Prompting (VSP) and Temporal Attention Regularization (TAR), the latter being our core contribution. Based on a systematic analysis, we discover that the temporal units in pretrained T2V models are crucial to control the video dynamics. Upon this finding, we propose a novel regularization technique to refine the temporal attention, enabling training-free longer video synthesis in a single inference pass. For prompts involving visual progression, we leverage LLMs to generate video synopsis - description of key visual states - based on the original prompt to provide better guidance along the temporal axis. We experimentally showcase the superiority of our method in synthesizing longer, visually appealing videos over open-sourced T2V models.

Deep Learning · Generative Models and Autoencoders

Alireza Ganjdanesh, Reza Shirkavand, Shangqian Gao, Heng Huang

Text-to-image (T2I) diffusion models have demonstrated impressive image generation capabilities. Still, their computational intensity prohibits resource-constrained organizations from deploying T2I models after fine-tuning them on their internal *target* data. While pruning techniques offer a potential solution to reduce the computational burden of T2I models, static pruning methods use the same pruned model for all input prompts, overlooking the varying capacity requirements of different prompts. Dynamic pruning addresses this issue by utilizing a separate sub-network for each prompt, but it prevents batch parallelism on GPUs. To overcome these limitations, we introduce Adaptive Prompt-Tailored Pruning (APTP), a novel prompt-based pruning method designed for T2I diffusion models. Central to our approach is a *prompt router* model, which learns to determine the required capacity for an input text prompt and routes it to an architecture code, given a total desired compute budget for prompts. Each architecture code represents a specialized model tailored to the prompts assigned to it, and the number of codes is a hyperparameter. We train the prompt router and architecture codes using contrastive learning, ensuring that similar prompts are mapped to nearby codes. Further, we employ optimal transport to prevent the codes from collapsing into a single one. We demonstrate APTP's effectiveness by pruning Stable Diffusion (SD) V2.1 using CC3M and COCO as *target* datasets. APTP outperforms the single-model pruning baselines in terms of FID, CLIP, and CMMD scores. Our analysis of the clusters learned by APTP reveals they are semantically meaningful. We also show that APTP can automatically discover previously empirically found challenging prompts for SD, *e.g.,* prompts for generating text images, assigning them to higher capacity codes.

Optimization · Sampling and Optimization

Sebastian Sanokowski, Wilhelm Berghammer, Haoyu Wang, Martin Ennemoser, Sepp Hochreiter, Sebastian Lehner

Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has demonstrated the potential of diffusion models in this domain. However, existing methods face limitations in memory scaling and thus the number of attainable diffusion steps since they require backpropagation through the entire generative process. To overcome these limitations we introduce two novel training methods for discrete diffusion samplers, one grounded in the policy gradient theorem and the other one leveraging Self-Normalized Neural Importance Sampling (SN-NIS). These methods yield memory-efficient training and achieve state-of-the-art results in unsupervised combinatorial optimization.Numerous scientific applications additionally require the ability of unbiased sampling. We introduce adaptations of SN-NIS and Neural Markov Chain Monte Carlo that enable for the first time the application of discrete diffusion models to this problem. We validate our methods on Ising model benchmarks and find that they outperform popular autoregressive approaches. Our work opens new avenues for applying diffusion models to a wide range of scientific applications in discrete domains that were hitherto restricted to exact likelihood models.

Applications · Everything Else

Koichi Saito, Dongjun Kim, Takashi Shibuya, Chieh-Hsin Lai, Zhi Zhong, Yuhta Takida, Yuki Mitsufuji

Sound content creation, essential for multimedia works such as video games and films, often involves extensive trial-and-error, enabling creators to semantically reflect their artistic ideas and inspirations, which evolve throughout the creation process, into the sound.Recent high-quality diffusion-based Text-to-Sound (T2S) generative models provide valuable tools for creators. However, these models often suffer from slow inference speeds, imposing an undesirable burden that hinders the trial-and-error process.While existing T2S distillation models address this limitation through $1$-step generation, the sample quality of $1$-step generation remains insufficient for production use.Additionally, while multi-step sampling in those distillation models improves sample quality itself, the semantic content changes due to their lack of deterministic sampling capabilities.Thus, developing a T2S generative model that allows creators to efficiently conduct trial-and-error while producing high-quality sound remains a key challenge.To address these issues, we introduce Sound Consistency Trajectory Models (SoundCTM), which allow flexible transitions between high-quality $1$-step sound generation and superior sound quality through multi-step deterministic sampling. This allows creators to efficiently conduct trial-and-error with $1$-step generation to semantically align samples with their intention, and subsequently refine sample quality with preserving semantic content through deterministic multi-step sampling.To develop SoundCTM, we reframe the CTM training framework, originally proposed in computer vision, and introduce a novel feature distance using the teacher network for a distillation loss. Additionally, while distilling classifier-free guided trajectories, we introduce a $\nu$-sampling, a new algorithm that offers another source of quality improvement. For the $\nu$-sampling, we simultaneously train both conditional and unconditional student models.For production-level generation, we scale up our model to 1B trainable parameters, making SoundCTM-DiT-1B the first large-scale distillation model in the sound community to achieve both promising high-quality $1$-step and multi-step full-band (44.1kHz) generation.Audio samples are available at \url{https://anonymus-soundctm.github.io/soundctm_iclr/}.

Deep Learning · Generative Models and Autoencoders

Yici Yan, Yichi Zhang, XIANGMING MENG, Zhizhen Zhao

Diffusion and flow matching models have recently been used to solve various linear inverse problems in image restoration, such as super-resolution and inpainting. Using a pre-trained diffusion or flow-matching model as a prior, most existing methods modify the reverse-time sampling process by incorporating the likelihood information from the measurement. However, they struggle in challenging scenarios, such as high measurement noise or severe ill-posedness. In this paper, we propose Flow with Interpolant Guidance (FIG), an algorithm where reverse-time sampling is efficiently guided with measurement interpolants through theoretically justified schemes. Experimentally, we demonstrate that FIG efficiently produces highly competitive results on a variety of linear image reconstruction tasks on natural image datasets, especially for challenging tasks. Our code is available at: https://riccizz.github.io/FIG/.