Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling (2404.12940v2)

Abstract: Conventional diffusion models typically relies 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 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 likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories, and demonstrate how the framework may be adopted for learning bridges between two distributions. The results underscores NFDM's versatility and its potential for a wide range of applications.

• The paper introduces a learnable forward process that broadens latent variable distributions beyond traditional Gaussian methods.
• The paper employs simulation-free, end-to-end optimization to achieve a tighter variational bound on negative log-likelihood.
• The paper demonstrates state-of-the-art performance on benchmarks like CIFAR-10 and ImageNet by streamlining generative dynamics.

Neural Flow Diffusion Models: Enriching Diffusion Modelling through Learnable Forward Processes

Introduction to Neural Flow Diffusion Models (NFDM)

Neural Flow Diffusion Models (NFDM) introduce a significant evolution in the field of diffusion models for generative machine learning, enhancing the flexibility and performance of these systems. Traditionally, diffusion models are limited by a predetermined Gaussian forward process. NFDM deviates from this norm by allowing the forward process to be entirely learnable, which both broadens the possible types of forward models that can be deployed and directly impacts the model's effectiveness in diverse generative tasks.

Key Contributions of NFDM

NFDM's core advancements and contributions can be encapsulated in the following points:

1. Integration of a Learnable Forward Process: NFDM facilitates the definition of a broader variety of latent variable distributions which can extend beyond simple Gaussian forms. This is achieved by permitting the forward process to be represented as a learnable function, increasing the adaptability and power of the model in handling complex distributions.
2. End-to-end Simulation-Free Optimization: The framework leverages a novel optimization approach that operates without the necessity for simulating the complete forward or reverse processes. This optimization strategy minimizes a variational upper bound on the negative log-likelihood, thereby enhancing computational efficiency.
3. State-of-the-Art Performance: NFDM was rigorously tested on standard datasets like CIFAR-10 and ImageNet, showcasing superior performance in terms of likelihood estimation when compared to existing models. This improvement is demonstrated by its ability to achieve lower negative log-likelihood scores.
4. Generative Dynamics with Custom Properties: One particularly notable aspect of NFDM is its ability to regulate and learn specific dynamics within the generation process, such as trajectories resembling straight lines which can simplify the generative path and reduce computational load.

Underlying Methodology

The methodology driving NFDM involves a detailed configuration of the forward process through a learnable distribution function, significantly differing from traditional methods that use a fixed Gaussian process. Here’s how NFDM diverges and the benefits entailed:

• Flexibility in Process Formulation: By allowing for a learnable forward process, NFDM can adapt its dynamics based on the specific requirements and complexities of the dataset it is trained on, as opposed to being restricted to a predefined pathway.
• Improved Variational Bound: The variational approach in optimizing the negative log-likelihood offers a tighter approximation to the true data distribution, facilitating more accurate generative modeling.
• Efficiency in Generation: NFDM’s capacity to learn specific characteristics of the generative dynamics, like straight-line trajectories, significantly streamlines the generative process, potentially reducing the time and computational resources required.

Experimental Results and Comparisons

Experimental evaluations demonstrate NFDM’s robust performance across various standard benchmarks. On datasets such as CIFAR-10 and ImageNet, NFDM consistently outperformed established models with respect to likelihood estimation metrics. The model showcases compelling improvements especially in handling high-dimensional and complex data distributions, attributing to its adaptive and flexible forward process.

Future Prospects and Improvements

Looking forward, NFDM sets a promising groundwork for the development of more dynamic and adaptive generative models. Further research could explore various parameterizations of the forward process, investigate novel optimization techniques, and perhaps extend the application of NFDM to other areas such as video and audio processing where complex data distributions are prevalent.

In conclusion, Neural Flow Diffusion Models mark a significant step forward in the capability and flexibility of generative diffusion models, paving the way for more sophisticated and efficient generative AI systems.