# Implicit Dynamical Flow Fusion (IDFF) for Generative Modeling

**Authors:** Mohammad R. Rezaei, Rahul G. Krishnan, Milos R. Popovic, Milad Lankarany  
**arXiv:** [2409.14599](https://arxiv.org/abs/2409.14599)  
**Date:** 2024-09-22  
**Summary page:** https://www.summarizepaper.com/en/paper/2409.14599v3/

## Key points

- Conditional Flow Matching (CFM) models successful in generating high-quality samples from a non-informative prior
- CFMs often require hundreds of network evaluations (NFE), making them slow and inefficient
- Implicit Dynamical Flow Fusion (IDFF) introduced to address the inefficiency issue
- IDFF reduces NFEs by a factor of ten compared to traditional CFMs while maintaining sample quality
- IDFF outperforms other models on time-series datasets modeling, including molecular simulation and sea surface temperature forecasting

## Summary

, , , , 

In the field of generative modeling, Conditional Flow Matching (CFM) models have been successful in generating high-quality samples from a non-informative prior. However, these models often require hundreds of network evaluations (NFE), making them slow and inefficient. To address this issue, a novel approach called Implicit Dynamical Flow Fusion (IDFF) has been proposed. IDFF introduces a new vector field with an additional momentum term that allows for longer sampling steps without compromising the fidelity of the generated distribution. Inspired by Hamiltonian Monte Carlo (HMC) algorithms, which leverage conservation properties of Hamiltonian dynamics, IDFF significantly reduces the number of network evaluations required during sample generation. By integrating a momentum term into the vector field of conditional flow models, IDFF is able to reduce NFEs by a factor of ten compared to traditional CFMs while maintaining sample quality. The effectiveness of IDFF has been demonstrated through experiments on standard benchmarks such as CIFAR-10 and CelebA for image generation tasks. Results show that IDFF achieves likelihood and quality performance comparable to CFMs and diffusion-based models with fewer NFEs. Additionally, IDFF outperforms other models on time-series datasets modeling, including molecular simulation and sea surface temperature forecasting. Figure 1 showcases the capabilities of IDFF in generating high-quality images across various datasets like CIFAR10, CelebA-64, ImageNet-64, LSUN-Bedroom, LSUN-Church, and CelebA-HQ with only 10 NFEs. The generated images demonstrate IDFF's ability to capture realistic visuals at different levels of complexity and resolution. Overall, the introduction of Implicit Dynamical Flow Fusion presents a significant advancement in generative modeling by enabling rapid sampling and efficient handling of image and time-series data generation tasks while maintaining high sample quality across different domains.