Causal inconsistency arises when the underlying causal graphs captured by generative models like \textit{Normalizing Flows} (NFs) are inconsistent with those specified in causal models like \textit{Struct Causal Models} (SCMs). This inconsistency can cause unwanted issues including the unfairness problem. Prior works to achieve causal consistency inevitably compromise the expressiveness of their models by disallowing hidden layers. In this work, we introduce a new approach: \textbf{C}ausally \textbf{C}onsistent \textbf{N}ormalizing \textbf{F}low (CCNF). To the best of our knowledge, CCNF is the first causally consistent generative model that can approximate any distribution with multiple layers. CCNF relies on two novel constructs: a sequential representation of SCMs and partial causal transformations. These constructs allow CCNF to inherently maintain causal consistency without sacrificing expressiveness. CCNF can handle all forms of causal inference tasks, including interventions and counterfactuals. Through experiments, we show that CCNF outperforms current approaches in causal inference. We also empirically validate the practical utility of CCNF by applying it to real-world datasets and show how CCNF addresses challenges like unfairness effectively.

In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective Lyapunov function. Despite this, connections between control theory and generative models in the literature are sparse, even though there are several machine learning applications with physically stable data points. In this paper, we focus on such data and a recent class of deep generative models called flow matching. We apply tools of stochastic stability for time-independent systems to flow matching models. In doing so, we characterize the space of flow matching models that are amenable to this treatment, as well as draw connections to other control theory principles. We demonstrate our theoretical results on two examples.

Continuous Normalizing Flows (CNFs) have emerged as promising deep generative models for a wide range of tasks thanks to their invertibility and exact likelihood estimation. However, conditioning CNFs on signals of interest for conditional image generation and downstream predictive tasks is inefficient due to the high-dimensional latent code generated by the model, which needs to be of the same size as the input data. In this paper, we propose InfoCNF, an efficient conditional CNF that partitions the latent space into a class-specific supervised code and an unsupervised code that shared among all classes for efficient use of labeled information. Since the partitioning strategy (slightly) increases the number of function evaluations (NFEs), InfoCNF also employs gating networks to learn the error tolerances of its ordinary differential equation (ODE) solvers for better speed and performance. We show empirically that InfoCNF improves the test accuracy over the baseline while yielding comparable likelihood scores and reducing the NFEs on CIFAR10. Furthermore, applying the same partitioning strategy in InfoCNF on time-series data helps improve extrapolation performance.