# Resistive Memory-based Neural Differential Equation Solver for Score-based Diffusion Model

arXiv: https://arxiv.org/abs/2404.05648 · HTML: https://mlsanity.com/paper/2404.05648/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 27 of its 74 references that are in the map.
- First posted on arXiv 8 Apr 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Fast ODE-based Sampling for Diffusion Models in Around 5 Steps](https://mlsanity.com/paper/2312.00094/) (2023)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates](https://mlsanity.com/paper/2008.10546/) (2020)
- [Diffusion Models in NLP: A Survey](https://mlsanity.com/paper/2303.07576/) (2023)
- [One-step regression and classification with crosspoint resistive memory arrays](https://mlsanity.com/paper/2005.01988/) (2020)
- [Geometry of Score Based Generative Models](https://mlsanity.com/paper/2302.04411/) (2023)
- [Gradient-based Neuromorphic Learning on Dynamical RRAM Arrays](https://mlsanity.com/paper/2206.12992/) (2022)

## Abstract (arXiv)

Human brains image complicated scenes when reading a novel. Replicating this imagination is one of the ultimate goals of AI-Generated Content (AIGC). However, current AIGC methods, such as score-based diffusion, are still deficient in terms of rapidity and efficiency. This deficiency is rooted in the difference between the brain and digital computers. Digital computers have physically separated storage and processing units, resulting in frequent data transfers during iterative calculations, incurring large time and energy overheads. This issue is further intensified by the conversion of inherently continuous and analog generation dynamics, which can be formulated by neural differential equations, into discrete and digital operations. Inspired by the brain, we propose a time-continuous and analog in-memory neural differential equation solver for score-based diffusion, employing emerging resistive memory. The integration of storage and computation within resistive memory synapses surmount the von Neumann bottleneck, benefiting the generative speed and energy efficiency. The closed-loop feedback integrator is time-continuous, analog, and compact, physically implementing an infinite-depth neural network. Moreover, the software-hardware co-design is intrinsically robust to analog noise. We experimentally validate our solution with 180 nm resistive memory in-memory computing macros. Demonstrating equivalent generative quality to the software baseline, our system achieved remarkable enhancements in generative speed for both unconditional and conditional generation tasks, by factors of 64.8 and 156.5, respectively. Moreover, it accomplished reductions in energy consumption by factors of 5.2 and 4.1. Our approach heralds a new horizon for hardware solutions in edge computing for generative AI applications.