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DFM: Interpolant-free Dual Flow Matching

Denis Gudovskiy, Tomoyuki Okuno, Yohei Nakata

TL;DR

The paper tackles the computational burden and interpolation biases in training continuous normalizing flows (CNFs) using flow matching (FM). It introduces interpolant-free dual flow matching (DFM), which learns both a forward and a reverse vector field and enforces bijectivity with a dedicated objective, enabling effective density estimation without interpolated paths. The approach achieves state-of-the-art results on the SMAP anomaly-detection benchmark compared to CNF and FM baselines, with notable gains in precision and F1 at modest additional cost. This has practical impact for robust density estimation and unsupervised anomaly detection in real-world time-series data.

Abstract

Continuous normalizing flows (CNFs) can model data distributions with expressive infinite-length architectures. But this modeling involves computationally expensive process of solving an ordinary differential equation (ODE) during maximum likelihood training. Recently proposed flow matching (FM) framework allows to substantially simplify the training phase using a regression objective with the interpolated forward vector field. In this paper, we propose an interpolant-free dual flow matching (DFM) approach without explicit assumptions about the modeled vector field. DFM optimizes the forward and, additionally, a reverse vector field model using a novel objective that facilitates bijectivity of the forward and reverse transformations. Our experiments with the SMAP unsupervised anomaly detection show advantages of DFM when compared to the CNF trained with either maximum likelihood or FM objectives with the state-of-the-art performance metrics.

DFM: Interpolant-free Dual Flow Matching

TL;DR

The paper tackles the computational burden and interpolation biases in training continuous normalizing flows (CNFs) using flow matching (FM). It introduces interpolant-free dual flow matching (DFM), which learns both a forward and a reverse vector field and enforces bijectivity with a dedicated objective, enabling effective density estimation without interpolated paths. The approach achieves state-of-the-art results on the SMAP anomaly-detection benchmark compared to CNF and FM baselines, with notable gains in precision and F1 at modest additional cost. This has practical impact for robust density estimation and unsupervised anomaly detection in real-world time-series data.

Abstract

Continuous normalizing flows (CNFs) can model data distributions with expressive infinite-length architectures. But this modeling involves computationally expensive process of solving an ordinary differential equation (ODE) during maximum likelihood training. Recently proposed flow matching (FM) framework allows to substantially simplify the training phase using a regression objective with the interpolated forward vector field. In this paper, we propose an interpolant-free dual flow matching (DFM) approach without explicit assumptions about the modeled vector field. DFM optimizes the forward and, additionally, a reverse vector field model using a novel objective that facilitates bijectivity of the forward and reverse transformations. Our experiments with the SMAP unsupervised anomaly detection show advantages of DFM when compared to the CNF trained with either maximum likelihood or FM objectives with the state-of-the-art performance metrics.

Paper Structure

This paper contains 5 sections, 12 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. CNF Preliminaries and Prior FM Methods
  3. The Proposed Interpolant-free Dual Flow Matching
  4. Experiments
  5. Conclusions

Figures (1)

  • Figure 1: The CFM (top) regresses the Gaussian-interpolated forward vector field by a neural network with the affine transformation$\phi_t({\bm{x}})$. Our DFM (bottom) has two neural networks with the free-form transformations with only the bijectivity objective ${\bm{x}}_t=\phi^{-1}_{\bm{\lambda}}(\phi_{\bm{\theta}}({\bm{x}}_t))$ for an arbitrary vector field and a probability path.