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Downsizing Diffusion Models for Cardinality Estimation

Xinhe Mu, Zhaoqi Zhou, Zaijiu Shang, Chuan Zhou, Gang Fu, Guiying Yan, Guoliang Li, Zhiming Ma

TL;DR

This work tackles the high-latency barrier of diffusion models for cardinality estimation by introducing ADC, a downsized diffusion framework that couples a Score Estimator, Density Estimator, and a GMM-Bayesnet-based Selectivity Estimator. It further extends with ADC+, which uses a lightweight classifier to bypass sampling for easy, high-volume queries, achieving sub-10ms latency and tiny storage footprints while maintaining high accuracy, including up to 10x better Q-error on complex multilateral distributions. The authors provide theoretical insights into score behavior as diffusion time approaches zero and convergence rates for large t, guiding parameter choices and enabling reliable operation in database systems. Experimental results on real-world and synthetic datasets show robust performance against state-of-the-art learned estimators, with ADC+ delivering the best trade-offs on most benchmarks and ADC offering strong robustness for challenging correlation structures.

Abstract

Learned cardinality estimation requires accurate model designs to capture the local characteristics of probability distributions. However, existing models may fail to accurately capture complex, multilateral dependencies between attributes. Diffusion models, meanwhile, can succeed in estimating image distributions with thousands of dimensions, making them promising candidates, but their heavy weight and high latency prohibit effective implementation. We seek to make diffusion models more lightweight by introducing Accelerated Diffusion Cardest (ADC), the first "downsized" diffusion model framework for efficient, high-precision cardinality estimation. ADC utilizes a hybrid architecture that integrates a Gaussian Mixture-Bayesnet selectivity estimator with a score-based density estimator to perform precise Monte Carlo integration. Addressing the issue of prohibitive inference latencies common in large generative models, we provide theoretical advancements concerning the asymptotic behavior of score functions as time $t$ approaches zero and convergence rate estimates as $t$ increases, enabling the adaptation of score-based diffusion models to the moderate dimensionalities and stringent latency requirements of database systems. Through experiments conducted against five learned estimators, including the state-of-the-art Naru, we demonstrate that ADC offer superior robustness when handling datasets with multilateral dependencies, which cannot be effectively summarized using pairwise or triple-wise correlations. In fact, ADC is 10 times more accurate than Naru on such datasets. Additionally, ADC achieves competitive accuracy comparable to Naru across all tested datasets while maintaining latency half that of Naru's and requiring minimal storage (<350KB) on most datasets.

Downsizing Diffusion Models for Cardinality Estimation

TL;DR

This work tackles the high-latency barrier of diffusion models for cardinality estimation by introducing ADC, a downsized diffusion framework that couples a Score Estimator, Density Estimator, and a GMM-Bayesnet-based Selectivity Estimator. It further extends with ADC+, which uses a lightweight classifier to bypass sampling for easy, high-volume queries, achieving sub-10ms latency and tiny storage footprints while maintaining high accuracy, including up to 10x better Q-error on complex multilateral distributions. The authors provide theoretical insights into score behavior as diffusion time approaches zero and convergence rates for large t, guiding parameter choices and enabling reliable operation in database systems. Experimental results on real-world and synthetic datasets show robust performance against state-of-the-art learned estimators, with ADC+ delivering the best trade-offs on most benchmarks and ADC offering strong robustness for challenging correlation structures.

Abstract

Learned cardinality estimation requires accurate model designs to capture the local characteristics of probability distributions. However, existing models may fail to accurately capture complex, multilateral dependencies between attributes. Diffusion models, meanwhile, can succeed in estimating image distributions with thousands of dimensions, making them promising candidates, but their heavy weight and high latency prohibit effective implementation. We seek to make diffusion models more lightweight by introducing Accelerated Diffusion Cardest (ADC), the first "downsized" diffusion model framework for efficient, high-precision cardinality estimation. ADC utilizes a hybrid architecture that integrates a Gaussian Mixture-Bayesnet selectivity estimator with a score-based density estimator to perform precise Monte Carlo integration. Addressing the issue of prohibitive inference latencies common in large generative models, we provide theoretical advancements concerning the asymptotic behavior of score functions as time approaches zero and convergence rate estimates as increases, enabling the adaptation of score-based diffusion models to the moderate dimensionalities and stringent latency requirements of database systems. Through experiments conducted against five learned estimators, including the state-of-the-art Naru, we demonstrate that ADC offer superior robustness when handling datasets with multilateral dependencies, which cannot be effectively summarized using pairwise or triple-wise correlations. In fact, ADC is 10 times more accurate than Naru on such datasets. Additionally, ADC achieves competitive accuracy comparable to Naru across all tested datasets while maintaining latency half that of Naru's and requiring minimal storage (<350KB) on most datasets.
Paper Structure (34 sections, 5 theorems, 70 equations, 3 figures, 2 tables, 2 algorithms)

This paper contains 34 sections, 5 theorems, 70 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Cardinality Estimation
  4. Problem Formulation
  5. Current Methods
  6. Why Diffusion Models?
  7. Score-Based Diffusion Models
  8. Introduction and Notations
  9. Forward and Backward process
  10. Error Analysis and Likelihood Evaluation
  11. The Score Estimator
  12. Model Choice
  13. Model Architecture Improvement: QuadNet
  14. Choosing Early Stopping Time
  15. The Density Estimator
  16. ...and 19 more sections

Key Result

theorem 1

See Appendix A for proof of all theorems Let $p_0$ be a probabilistic distribution and $\{p_t|t\in[0,T]\}$ be a family of distributions derived by perturbing $p_0$ using the SDE (forward) from time 0 to time $T$. Let $k(t)=e^{\int_0^t\alpha(s)ds}$, and $\sigma^2(t)$ be the solution of the initial va then, for each choice of $\alpha$ and $\beta$, it would hold that where $\tau$ in $\mathbb{R}^d$ i

Figures (3)

  • Figure 1: ADC's training and inference framework.
  • Figure 2: The 2d toy dataset for testing (left) and the loss curve of different score matching network architectures (right). "Ideal network" (red) refers to Quadnet while Network 1 (blue), 2 (yellow), and 3 (green) possess only the quadratic, linear, and constant scaling module, respectively.
  • Figure 3: Performance of ADC and ADC- with respect to GMM-estimated selectivity ($x$-axis) and query volume ($y$-axis), both shown on a log scale

Theorems & Definitions (5)

  • theorem 1
  • theorem 2
  • theorem 3
  • theorem 4
  • theorem 5