Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching

Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly compute image likelihoods from a learned flow, making them enticing candidates as priors for downstream tasks such as inverse problems. In particular, a natural approach would be to incorporate such image probabilities in a maximum-a-posteriori (MAP) estimation problem. A major obstacle, however, lies in the slow computation of the log-likelihood, as it requires backpropagating through an ODE solver, which can be prohibitively slow for high-dimensional problems. In this work, we propose an iterative algorithm to approximate the MAP estimator efficiently to solve a variety of linear inverse problems. Our algorithm is mathematically justified by the observation that the MAP objective can be approximated by a sum of $N$ ``local MAP'' objectives, where $N$ is the number of function evaluations. By leveraging Tweedie's formula, we show that we can perform gradient steps to sequentially optimize these objectives. We validate our approach for various linear inverse problems, such as super-resolution, deblurring, inpainting, and compressed sensing, and demonstrate that we can outperform other methods based on flow matching.

Atlas3D: Physically Constrained Self-Supporting Text-to-3D for Simulation and Fabrication

Existing diffusion-based text-to-3D generation methods primarily focus on producing visually realistic shapes and appearances, often neglecting the physical constraints necessary for downstream tasks. Generated models frequently fail to maintain balance when placed in physics-based simulations or 3D printed. This balance is crucial for satisfying user design intentions in interactive gaming, embodied AI, and robotics, where stable models are needed for reliable interaction. Additionally, stable models ensure that 3D-printed objects, such as figurines for home decoration, can stand on their own without requiring additional supports. To fill this gap, we introduce Atlas3D, an automatic and easy-to-implement method that enhances existing Score Distillation Sampling (SDS)-based text-to-3D tools. Atlas3D ensures the generation of self-supporting 3D models that adhere to physical laws of stability under gravity, contact, and friction. Our approach combines a novel differentiable simulation-based loss function with physically inspired regularization, serving as either a refinement or a post-processing module for existing frameworks. We verify Atlas3D's efficacy through extensive generation tasks and validate the resulting 3D models in both simulated and real-world environments.

An Investigation of Conformal Isometry Hypothesis for Grid Cells

This paper investigates the conformal isometry hypothesis as a potential explanation for the emergence of hexagonal periodic patterns in the response maps of grid cells. The hypothesis posits that the activities of the population of grid cells form a high-dimensional vector in the neural space, representing the agent's self-position in 2D physical space. As the agent moves in the 2D physical space, the vector rotates in a 2D manifold in the neural space, driven by a recurrent neural network. The conformal isometry hypothesis proposes that this 2D manifold in the neural space is a conformally isometric embedding of the 2D physical space, in the sense that local displacements of the vector in neural space are proportional to local displacements of the agent in the physical space. Thus the 2D manifold forms an internal map of the 2D physical space, equipped with an internal metric. In this paper, we conduct numerical experiments to show that this hypothesis underlies the hexagon periodic patterns of grid cells. We also conduct theoretical analysis to further support this hypothesis. In addition, we propose a conformal modulation of the input velocity of the agent so that the recurrent neural network of grid cells satisfies the conformal isometry hypothesis automatically. To summarize, our work provides numerical and theoretical evidences for the conformal isometry hypothesis for grid cells and may serve as a foundation for further development of normative models of grid cells and beyond.

EM Distillation for One-step Diffusion Models

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation with very few sampling steps, reliance on training data access, or mode-seeking optimization that may fail to capture the full distribution. We propose EM Distillation (EMD), a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of perceptual quality. Our approach is derived through the lens of Expectation-Maximization (EM), where the generator parameters are updated using samples from the joint distribution of the diffusion teacher prior and inferred generator latents. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process. We further reveal an interesting connection of our method with existing methods that minimize mode-seeking KL. EMD outperforms existing one-step generative methods in terms of FID scores on ImageNet-64 and ImageNet-128, and compares favorably with prior work on distilling text-to-image diffusion models.

Latent Energy-Based Odyssey: Black-Box Optimization via Expanded Exploration in the Energy-Based Latent Space

Offline Black-Box Optimization (BBO) aims at optimizing a black-box function using the knowledge from a pre-collected offline dataset of function values and corresponding input designs. However, the high-dimensional and highly-multimodal input design space of black-box function pose inherent challenges for most existing methods that model and operate directly upon input designs. These issues include but are not limited to high sample complexity, which relates to inaccurate approximation of black-box function; and insufficient coverage and exploration of input design modes, which leads to suboptimal proposal of new input designs. In this work, we consider finding a latent space that serves as a compressed yet accurate representation of the design-value joint space, enabling effective latent exploration of high-value input design modes. To this end, we formulate an learnable energy-based latent space, and propose Noise-intensified Telescoping density-Ratio Estimation (NTRE) scheme for variational learning of an accurate latent space model without costly Markov Chain Monte Carlo. The optimization process is then exploration of high-value designs guided by the learned energy-based model in the latent space, formulated as gradient-based sampling from a latent-variable-parameterized inverse model. We show that our particular parameterization encourages expanded exploration around high-value design modes, motivated by inversion thinking of a fundamental result of conditional covariance matrix typically used for variance reduction. We observe that our method, backed by an accurately learned informative latent space and an expanding-exploration model design, yields significant improvements over strong previous methods on both synthetic and real world datasets such as the design-bench suite.

Watermarking Generative Tabular Data

In this paper, we introduce a simple yet effective tabular data watermarking mechanism with statistical guarantees. We show theoretically that the proposed watermark can be effectively detected, while faithfully preserving the data fidelity, and also demonstrates appealing robustness against additive noise attack. The general idea is to achieve the watermarking through a strategic embedding based on simple data binning. Specifically, it divides the feature's value range into finely segmented intervals and embeds watermarks into selected ``green list" intervals. To detect the watermarks, we develop a principled statistical hypothesis-testing framework with minimal assumptions: it remains valid as long as the underlying data distribution has a continuous density function. The watermarking efficacy is demonstrated through rigorous theoretical analysis and empirical validation, highlighting its utility in enhancing the security of synthetic and real-world datasets.

Object-Conditioned Energy-Based Attention Map Alignment in Text-to-Image Diffusion Models

Text-to-image diffusion models have shown great success in generating high-quality text-guided images. Yet, these models may still fail to semantically align generated images with the provided text prompts, leading to problems like incorrect attribute binding and/or catastrophic object neglect. Given the pervasive object-oriented structure underlying text prompts, we introduce a novel object-conditioned Energy-Based Attention Map Alignment (EBAMA) method to address the aforementioned problems. We show that an object-centric attribute binding loss naturally emerges by approximately maximizing the log-likelihood of a $z$-parameterized energy-based model with the help of the negative sampling technique. We further propose an object-centric intensity regularizer to prevent excessive shifts of objects attention towards their attributes. Extensive qualitative and quantitative experiments, including human evaluation, on several challenging benchmarks demonstrate the superior performance of our method over previous strong counterparts. With better aligned attention maps, our approach shows great promise in further enhancing the text-controlled image editing ability of diffusion models.

LLM3:Large Language Model-based Task and Motion Planning with Motion Failure Reasoning

Conventional Task and Motion Planning (TAMP) approaches rely on manually crafted interfaces connecting symbolic task planning with continuous motion generation. These domain-specific and labor-intensive modules are limited in addressing emerging tasks in real-world settings. Here, we present LLM^3, a novel Large Language Model (LLM)-based TAMP framework featuring a domain-independent interface. Specifically, we leverage the powerful reasoning and planning capabilities of pre-trained LLMs to propose symbolic action sequences and select continuous action parameters for motion planning. Crucially, LLM^3 incorporates motion planning feedback through prompting, allowing the LLM to iteratively refine its proposals by reasoning about motion failure. Consequently, LLM^3 interfaces between task planning and motion planning, alleviating the intricate design process of handling domain-specific messages between them. Through a series of simulations in a box-packing domain, we quantitatively demonstrate the effectiveness of LLM^3 in solving TAMP problems and the efficiency in selecting action parameters. Ablation studies underscore the significant contribution of motion failure reasoning to the success of LLM^3. Furthermore, we conduct qualitative experiments on a physical manipulator, demonstrating the practical applicability of our approach in real-world settings.

Dual-Space Optimization: Improved Molecule Sequence Design by Latent Prompt Transformer

Designing molecules with desirable properties, such as drug-likeliness and high binding affinities towards protein targets, is a challenging problem. In this paper, we propose the Dual-Space Optimization (DSO) method that integrates latent space sampling and data space selection to solve this problem. DSO iteratively updates a latent space generative model and a synthetic dataset in an optimization process that gradually shifts the generative model and the synthetic data towards regions of desired property values. Our generative model takes the form of a Latent Prompt Transformer (LPT) where the latent vector serves as the prompt of a causal transformer. Our extensive experiments demonstrate effectiveness of the proposed method, which sets new performance benchmarks across single-objective, multi-objective and constrained molecule design tasks.

Efficient and Scalable Fine-Tune of Language Models for Genome Understanding

Although DNA foundation models have advanced the understanding of genomes, they still face significant challenges in the limited scale and diversity of genomic data. This limitation starkly contrasts with the success of natural language foundation models, which thrive on substantially larger scales. Furthermore, genome understanding involves numerous downstream genome annotation tasks with inherent data heterogeneity, thereby necessitating more efficient and robust fine-tuning methods tailored for genomics. Here, we present \textsc{Lingo}: \textsc{L}anguage prefix f\textsc{In}e-tuning for \textsc{G}en\textsc{O}mes. Unlike DNA foundation models, \textsc{Lingo} strategically leverages natural language foundation models' contextual cues, recalibrating their linguistic knowledge to genomic sequences. \textsc{Lingo} further accommodates numerous, heterogeneous downstream fine-tune tasks by an adaptive rank sampling method that prunes and stochastically reintroduces pruned singular vectors within small computational budgets. Adaptive rank sampling outperformed existing fine-tuning methods on all benchmarked 14 genome understanding tasks, while requiring fewer than 2\% of trainable parameters as genomic-specific adapters. Impressively, applying these adapters on natural language foundation models matched or even exceeded the performance of DNA foundation models. \textsc{Lingo} presents a new paradigm of efficient and scalable genome understanding via genomic-specific adapters on language models.