Creativity serves as a cornerstone for societal progress and innovation. With the rise of advanced generative AI models capable of tasks once reserved for human creativity, the study of AI's creative potential becomes imperative for its responsible development and application. In this paper, we prove in theory that AI can be as creative as humans under the condition that it can properly fit the data generated by human creators. Therefore, the debate on AI's creativity is reduced into the question of its ability to fit a sufficient amount of data. To arrive at this conclusion, this paper first addresses the complexities in defining creativity by introducing a new concept called Relative Creativity. Rather than attempting to define creativity universally, we shift the focus to whether AI can match the creative abilities of a hypothetical human. The methodological shift leads to a statistically quantifiable assessment of AI's creativity, term Statistical Creativity. This concept, statistically comparing the creative abilities of AI with those of specific human groups, facilitates theoretical exploration of AI's creative potential. Our analysis reveals that by fitting extensive conditional data without marginalizing out the generative conditions, AI can emerge as a hypothetical new creator. The creator possesses the same creative abilities on par with the human creators it was trained on. Building on theoretical findings, we discuss the application in prompt-conditioned autoregressive models, providing a practical means for evaluating creative abilities of generative AI models, such as Large Language Models (LLMs). Additionally, this study provides an actionable training guideline, bridging the theoretical quantification of creativity with practical model training.

Creating accurate and geologically realistic reservoir facies based on limited measurements is crucial for field development and reservoir management, especially in the oil and gas sector. Traditional two-point geostatistics, while foundational, often struggle to capture complex geological patterns. Multi-point statistics offers more flexibility, but comes with its own challenges. With the rise of Generative Adversarial Networks (GANs) and their success in various fields, there has been a shift towards using them for facies generation. However, recent advances in the computer vision domain have shown the superiority of diffusion models over GANs. Motivated by this, a novel Latent Diffusion Model is proposed, which is specifically designed for conditional generation of reservoir facies. The proposed model produces high-fidelity facies realizations that rigorously preserve conditioning data. It significantly outperforms a GAN-based alternative.

As a widely recognized approach to deep generative modeling, Variational Auto-Encoders (VAEs) still face challenges with the quality of generated images, often presenting noticeable blurriness. This issue stems from the unrealistic assumption that approximates the conditional data distribution, $p(\textbf{x} | \textbf{z})$, as an isotropic Gaussian. In this paper, we propose a novel solution to address these issues. We illustrate how one can extract a latent space from a pre-existing diffusion model by optimizing an encoder to maximize the marginal data log-likelihood. Furthermore, we demonstrate that a decoder can be analytically derived post encoder-training, employing the Bayes rule for scores. This leads to a VAE-esque deep latent variable model, which discards the need for Gaussian assumptions on $p(\textbf{x} | \textbf{z})$ or the training of a separate decoder network. Our method, which capitalizes on the strengths of pre-trained diffusion models and equips them with latent spaces, results in a significant enhancement to the performance of VAEs.

Background and objective: In the intensive care unit (ICU), vital sign monitoring is critical, and an accurate predictive system is required. This study will create a novel model to forecast Heart Rate (HR), Systolic Blood Pressure (SBP), and Diastolic Blood Pressure (DBP) in ICU. These vital signs are crucial for prompt interventions for patients. We extracted $24,886$ ICU stays from the MIMIC-III database, which contains data from over $46$ thousand patients, to train and test the model. Methods: The model proposed in this study, areansformerin intensive careabilistic Model for Sparse Time Series Forecasting (TDSTF), uses a deep learning technique called the Transformer. The TDSTF model showed state-of-the-art performance in predicting vital signs in the ICU, outperforming other models' ability to predict distributions of vital signs and being more computationally efficient. The code is available at https://github.com/PingChang818/TDSTF. Results: The results of the study showed that TDSTF achieved a Normalized Average Continuous Ranked Probability Score (NACRPS) of $0.4438$ and a Mean Squared Error (MSE) of $0.4168$, an improvement of $18.9\%$ and $34.3\%$ over the best baseline model, respectively. Conclusion: In conclusion, TDSTF is an effective and efficient solution for forecasting vital signs in the ICU, and it shows a significant improvement compared to other models in the field.

Besides reproducing tabular data properties of standalone tables, synthetic relational databases also require modeling the relationships between related tables. In this paper, we propose the Row Conditional-Tabular Generative Adversarial Network (RC-TGAN), a novel generative adversarial network (GAN) model that extends the tabular GAN to support modeling and synthesizing relational databases. The RC-TGAN models relationship information between tables by incorporating conditional data of parent rows into the design of the child table's GAN. We further extend the RC-TGAN to model the influence that grandparent table rows may have on their grandchild rows, in order to prevent the loss of this connection when the rows of the parent table fail to transfer this relationship information. The experimental results, using eight real relational databases, show significant improvements in the quality of the synthesized relational databases when compared to the benchmark system, demonstrating the effectiveness of the RC-TGAN in preserving relationships between tables of the original database.