The primary goal of generative artificial intelligence (AI) models is to create realistic and high-quality data across various formats, including images, audio, and video, by identifying patterns within large datasets. These models possess the ability to mimic complex data distributions, enabling them to generate synthetic content that closely resembles the original samples. Among these, diffusion models have become a popular type of generative model, successfully producing images and videos by progressively reversing a sequence of added noise, ultimately achieving high-fidelity outputs. However, a notable drawback of diffusion models is their cumbersome sampling process, which typically requires dozens or even hundreds of steps to complete. This results in significant computational and time costs, making the limitation especially prominent in scenarios that demand rapid sampling or large-scale sample generation, such as real-time applications or extensive deployments.

One of the main challenges diffusion models face during the sampling process is the computational burden. This arises from the high computational costs required to systematically reverse the noise sequence, as well as errors introduced when discretizing time intervals. To address this issue, continuous-time diffusion models have emerged. These models eliminate the need for time intervals, thereby reducing sampling errors. However, due to instability issues during training, continuous-time models have not been widely adopted. This instability makes training these models on large or complex datasets difficult, thereby hindering their adoption and development in areas where computational efficiency is crucial.

To enhance the efficiency of diffusion models, researchers have recently developed a range of methods, including direct distillation, adversarial distillation, progressive distillation, and Variational Score Distillation (VSD). These methods show potential in accelerating the sampling process or improving sample quality but also face practical challenges such as high computational overhead, complex training setups, and scalability limitations. For example, direct distillation requires training from scratch, increasing time and resource costs; adversarial distillation often struggles with stability and consistency issues when using Generative Adversarial Network (GAN) architectures; while progressive distillation and VSD are effective for short-step models, they typically produce samples with limited diversity or fewer details, especially at higher guidance levels.

A research team at OpenAI introduced a new framework called TrigFlow, designed to streamline, stabilize, and scale continuous-time consistency models (CM). This framework specifically targets the instability issues in training continuous-time models by improving model parameterization, network architecture, and training objectives, thereby simplifying the training process. TrigFlow unifies diffusion and consistency models, identifying and mitigating the primary sources of instability, enabling the model to reliably handle continuous-time tasks. Even when scaled to large datasets like ImageNet, the model achieves high-quality sampling at minimal computational costs. Utilizing TrigFlow, the team successfully trained a 1.5 billion-parameter model that achieved high-quality scores with a two-step sampling process, while keeping computational costs lower than existing diffusion methods.

The core of TrigFlow lies in the mathematical redefinition that simplifies the probability flow ordinary differential equation (ODE) used during sampling. This enhancement combines adaptive group normalization with an adaptive weighted update objective function, stabilizing the training process and allowing the model to run continuously without being affected by discretization errors. Additionally, the time-conditioned approach in the network architecture reduces dependence on complex computations, making the model’s scalability feasible. The reconstructed training objective progressively anneals key terms within the model, enabling faster stabilization and unprecedented scaling.

The model, named “sCM” (Simple, Stable, and Scalable Consistency Model), demonstrates results comparable to state-of-the-art diffusion models. For instance, on the CIFAR-10 dataset, sCM achieved a Fréchet Inception Distance (FID) of 2.06; on ImageNet 64×64, it reached 1.48; and on ImageNet 512×512, it attained 1.88. These achievements significantly narrow the gap with leading diffusion models, while sCM utilizes only a two-step sampling process. Compared to previous methods that require more steps, the two-step model improved FID by nearly 10%, marking a substantial increase in sampling efficiency. The TrigFlow framework makes significant progress in model scalability and computational efficiency.

This study offers several key insights. Firstly, meticulously constructed continuous-time models can address the computational inefficiencies and limitations of traditional diffusion models. Secondly, by implementing TrigFlow, researchers have stabilized continuous-time CMs and scaled them to larger datasets and parameter sizes with minimal computational compromises.

1. Stability of Continuous-Time Models: TrigFlow introduces stability to continuous-time consistency models, a historically challenging area, ensuring that the training process does not frequently encounter instability risks.
2. Scalability: The model successfully scales to 1.5 billion parameters, making it the largest continuous-time consistency model of its kind and suitable for high-resolution data generation.
3. Efficient Sampling: With just two sampling steps, the sCM model achieves FID scores comparable to models that require extensive computational resources. It achieved 2.06 on CIFAR-10, 1.48 on ImageNet 64×64, and 1.88 on ImageNet 512×512.
4. Computational Efficiency: The adaptive weighting and simplified time conditioning within the TrigFlow framework make the model resource-efficient, reducing the need for computation-intensive sampling. This enhancement may improve the applicability of diffusion models in real-time and large-scale environments.

In summary, this research marks a pivotal advancement in generative model training. Through the TrigFlow framework, the research team has overcome issues related to stability, scalability, and sampling efficiency. OpenAI’s TrigFlow architecture and sCM model effectively address the main challenges of continuous-time consistency models, offering a stable and scalable solution. This approach matches the performance and quality of top-tier diffusion models while significantly lowering computational demands.