Conventional diffusion models often rely on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the standard linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihoods across a range of image generation tasks. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories, and demonstrate how the framework can be adopted for learning bridges between two distributions. The results underscores NFDM's versatility and its potential for a wide range of applications.

Diffusion probabilistic models have made their way into a number of high-profile applications since their inception. In particular, there has been a wave of research into using diffusion models in the prediction and design of biomolecular structures and sequences. Their growing ubiquity makes it imperative for researchers in these fields to understand them. This paper serves as a general overview for the theory behind these models and the current state of research. We first introduce diffusion models and discuss common motifs used when applying them to biomolecules. We then present the significant outcomes achieved through the application of these models in generative and predictive tasks. This survey aims to provide readers with a comprehensive understanding of the increasingly critical role of diffusion models.

The seven-valued logic considered in this paper naturally arises within the rough set framework, allowing to distinguish vagueness due to imprecision from ambiguity due to coarseness. Recently, we discussed its utility for reasoning about data describing multi-attribute classification of objects. We also showed that this logic contains, as a particular case, the celebrated Belnap four-valued logic. Here, we present how the seven-valued logic, as well as the other logics that derive from it, can be used to represent preferences in the domain of Multiple Criteria Decision Aiding (MCDA). In particular, we propose new forms of outranking and value function preference models that aggregate multiple criteria taking into account imperfect preference information. We demonstrate that our approach effectively addresses common challenges in preference modeling for MCDA, such as uncertainty, imprecision, and ill-determination of performances and preferences. To this end, we present a specific procedure to construct a seven-valued preference relation and use it to define recommendations that consider robustness concerns by utilizing multiple outranking or value functions representing the decision maker s preferences. Moreover, we discuss the main properties of the proposed seven-valued preference structure and compare it with current approaches in MCDA, such as ordinal regression, robust ordinal regression, stochastic multiattribute acceptability analysis, stochastic ordinal regression, and so on. We illustrate and discuss the application of our approach using a didactic example. Finally, we propose directions for future research and potential applications of the proposed methodology.

In an era of rapidly advancing data-driven applications, there is a growing demand for data in both research and practice. Synthetic data have emerged as an alternative when no real data is available (e.g., due to privacy regulations). Synthesizing tabular data presents unique and complex challenges, especially handling (i) missing values, (ii) dataset imbalance, (iii) diverse column types, and (iv) complex data distributions, as well as preserving (i) column correlations, (ii) temporal dependencies, and (iii) integrity constraints (e.g., functional dependencies) present in the original dataset. While substantial progress has been made recently in the context of generational models, there is no one-size-fits-all solution for tabular data today, and choosing the right tool for a given task is therefore no trivial task. In this paper, we survey the state of the art in Tabular Data Synthesis (TDS), examine the needs of users by defining a set of functional and non-functional requirements, and compile the challenges associated with meeting those needs. In addition, we evaluate the reported performance of 36 popular research TDS tools about these requirements and develop a decision guide to help users find suitable TDS tools for their applications. The resulting decision guide also identifies significant research gaps.

We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem. Equipped with these tools, we propose a simulation-free flow-based method for conditional generative modeling. Our method couples an arbitrary source distribution to a specified target distribution through a triangular COT plan, and a conditional generative model is obtained by approximating the geodesic path of measures induced by this COT plan. Our theory and methods are applicable in infinite-dimensional settings, making them well suited for a wide class of Bayesian inverse problems. Empirically, we demonstrate that our method is competitive on several challenging conditional generation tasks, including an infinite-dimensional inverse problem.

This paper introduces DiffPuter, an iterative method for missing data imputation that leverages the Expectation-Maximization (EM) algorithm and Diffusion Models. By treating missing data as hidden variables that can be updated during model training, we frame the missing data imputation task as an EM problem. During the M-step, DiffPuter employs a diffusion model to learn the joint distribution of both the observed and currently estimated missing data. In the E-step, DiffPuter re-estimates the missing data based on the conditional probability given the observed data, utilizing the diffusion model learned in the M-step. Starting with an initial imputation, DiffPuter alternates between the M-step and E-step until convergence. Through this iterative process, DiffPuter progressively refines the complete data distribution, yielding increasingly accurate estimations of the missing data. Our theoretical analysis demonstrates that the unconditional training and conditional sampling processes of the diffusion model align precisely with the objectives of the M-step and E-step, respectively. Empirical evaluations across 10 diverse datasets and comparisons with 16 different imputation methods highlight DiffPuter's superior performance. Notably, DiffPuter achieves an average improvement of 8.10% in MAE and 5.64% in RMSE compared to the most competitive existing method.

Natural language is structured hierarchically: words are grouped into phrases or constituents, which can be further grouped to form higher-level phrases up to the full sentence. How well do the neural network models trained on language data learn this phrase structure of human language has been a subject of great interest. A flurry of past work have shown that syntax trees can be recovered from recurrent neural network (RNN) and transformer-based models trained on large-scale language corpora (Tenney et al., 2019, Peters et al., 2018, Lin et al., 2019, Wu et al., 2020). While these studies provide useful evidence of the aforementioned phenomenon, they do not shed light on the architectural choices, training paradigms or dataset characteristics that lead models to learn the phrase structure of language. A useful tool to understand these model and dataset specific properties is through the test for hierarchical generalization, i.e., evaluating the capability of a model to generalize to novel syntactic forms, which were unseen during training. A classic problem to test for hierarchical generalization is question formation, where given a declarative sentence, e.g., My walrus does move the dogs that do wait., the task is to transform it into a question: Does my walrus move the dogs that do wait? The task is accomplished by moving one auxiliary verb to the front. The correct choice to move does in this example (rather than do), is predicted both by a hierarchical rule based on the phrase-structure syntax of the sentence, and by a linear rule that says to move the first auxiliary. Hence, as a test for hierarchical generalization, we can ask, for neural networks trained from scratch on data that is consistent with both hierarchical and linear rules (i.e.,

We prove that the combination of a target network and over-parameterized linear function approximation establishes a weaker convergence condition for bootstrapped value estimation in certain cases, even with off-policy data. Our condition is naturally satisfied for expected updates over the entire state-action space or learning with a batch of complete trajectories from episodic Markov decision processes. Notably, using only a target network or an over-parameterized model does not provide such a convergence guarantee. Additionally, we extend our results to learning with truncated trajectories, showing that convergence is achievable for all tasks with minor modifications, akin to value truncation for the final states in trajectories. Our primary result focuses on temporal difference estimation for prediction, providing high-probability value estimation error bounds and empirical analysis on Baird's counterexample and a Four-room task. Furthermore, we explore the control setting, demonstrating that similar convergence conditions apply to Q-learning.

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized sampling of the posterior over data, $\mathbf{x}\sim p^{\rm post}(\mathbf{x})\propto p(\mathbf{x})r(\mathbf{x})$, in a model that consists of a diffusion generative model prior $p(\mathbf{x})$ and a black-box constraint or likelihood function $r(\mathbf{x})$. We state and prove the asymptotic correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases. Relative trajectory balance arises from the generative flow network perspective on diffusion models, which allows the use of deep reinforcement learning techniques to improve mode coverage. Experiments illustrate the broad potential of unbiased inference of arbitrary posteriors under diffusion priors: in vision (classifier guidance), language (infilling under a discrete diffusion LLM), and multimodal data (text-to-image generation). Beyond generative modeling, we apply relative trajectory balance to the problem of continuous control with a score-based behavior prior, achieving state-of-the-art results on benchmarks in offline reinforcement learning.

Large language models (LLMs) like transformers have impressive in-context learning (ICL) capabilities; they can generate predictions for new queries based on input-output sequences in prompts without parameter updates. While many theories have attempted to explain ICL, they often focus on structured training data similar to ICL tasks, such as regression. In practice, however, these models are trained in an unsupervised manner on unstructured text data, which bears little resemblance to ICL tasks. To this end, we investigate how ICL emerges from unsupervised training on unstructured data. The key observation is that ICL can arise simply by modeling co-occurrence information using classical language models like continuous bag of words (CBOW), which we theoretically prove and empirically validate. Furthermore, we establish the necessity of positional information and noise structure to generalize ICL to unseen data. Finally, we present instances where ICL fails and provide theoretical explanations; they suggest that the ICL ability of LLMs to identify certain tasks can be sensitive to the structure of the training data.