DiffNMR3: Advancing NMR Resolution Beyond Instrumental Limits

TL;DR

We address the challenge of NMR frequency-resolution limits imposed by instrument field strength by introducing MSSR, a diffusion-model–based multi-scale super-resolution method that reconstructs high-field spectra from low-field data in the frequency domain. The approach employs a conditional UNet within a diffusion framework, using time-step and upscaling-factor conditioning along with the low-resolution spectrum to generate high-resolution outputs. Across the ARTINA dataset, MSSR demonstrates superior global and local reconstruction fidelity compared with per-factor baselines, achieving multi-scale SR with a 14-factor spectrum range. This methodology democratizes access to high-resolution NMR by delivering high-field-like detail on affordable, lower-field instruments, with potential integration into accelerated acquisition strategies and higher-dimensional NMR analyses.

Abstract

Nuclear Magnetic Resonance (NMR) spectroscopy is a crucial analytical technique used for molecular structure elucidation, with applications spanning chemistry, biology, materials science, and medicine. However, the frequency resolution of NMR spectra is limited by the "field strength" of the instrument. High-field NMR instruments provide high-resolution spectra but are prohibitively expensive, whereas lower-field instruments offer more accessible, but lower-resolution, results. This paper introduces an AI-driven approach that not only enhances the frequency resolution of NMR spectra through super-resolution techniques but also provides multi-scale functionality. By leveraging a diffusion model, our method can reconstruct high-field spectra from low-field NMR data, offering flexibility in generating spectra at varying magnetic field strengths. These reconstructions are comparable to those obtained from high-field instruments, enabling finer spectral details and improving molecular characterization. To date, our approach is one of the first to overcome the limitations of instrument field strength, achieving NMR super-resolution through AI. This cost-effective solution makes high-resolution analysis accessible to more researchers and industries, without the need for multimillion-dollar equipment.

Figures (6)

• Figure 1: The backbone of our MSSR approach. The UNet architecture unetAttentionUnet is an encoder-decoder structure. The model consists of a series of blocks for downsampling and upsampling, which form a U-shape. In our MSSR approach, the noisy high-resolution spectrum and the low-resolution spectrum are first concatenated and fed to the first layer of the model and then forwarded sequentially through different blocks until the final outputs. The upscaling factor and timestep embeddings are summed and inputted to each block independently.
• Figure 2: Our MSSR pipeline. In the diffusion process, the original NMR spectrum $x_0$ (high-resolution spectrum) is gradually corrupted by the Gaussian noise. After a total number of time steps $T$ in the diffusion process, the output is a noisy high-resolution spectrum denoted by $x_T$. $t$ represents the current time step. In the denoising process, an equally weighted sequence of UNets $p_{\theta}$, is trained to predict a denoised variant of their input $x_t$, where $x_t$ is a noisy version of the input $x_0$. $x_{LR}$ represents the low-resolution spectrum. $f$ is the upscaling factor representing the ratio of high resolution to low resolution. At the end of the denoising process, the high-resolution spectrum denoted by $\widehat{x_0}$ is reconstructed. The input of the UNet is the noisy spectrum $x_T$ at time step $T$ or the intermediate denoised spectrum (denoted by $\widehat{x_t}$) at time step $t$ where $t \in \{1,\dots,T-1\}$. The conditional inputs are the upscaling factor $f$, the time step $t$, and the low-resolution spectrum $x_{LR}$. Note that the architecture of the conditional UNet is detailed in Fig. \ref{['fig:unet']}.
• Figure 3: A: Original spectrum. B: Low-resolution spectrum (with upscaling factor $f=2$). C: MSSR. D: Baseline.
• Figure 4: Global metrics. We investigate the Mean Squared Error (MSE) and the Coefficient of Determination ($R^2$). These metrics can measure the overall alignment and similarity between the original spectrum and the reconstructed spectrum. MSE: the lower the better. $R^2$ the higher the better.
• Figure 5: Local metrics. We list the peak-focused metrics since the peaks are critical for identifying compound features. For the $R^2$ of peaks: the higher the better, for the other metrics: the lower the better.