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arxiv: 2606.27094 · v1 · pith:XR5AJPRSnew · submitted 2026-06-25 · ⚛️ physics.ao-ph

Learning Climate Variability from Scarce Data with Diffusion Models: A Test Case for ENSO

Lluis Palma , Vincent Verjans , Amanda Duarte , Albert Soret , Markus Donat This is my paper

Pith reviewed 2026-06-26 01:55 UTC · model grok-4.3

classification ⚛️ physics.ao-ph
keywords diffusion modelsENSOclimate variabilityscarce datapre-trainingCMIP6Linear Inverse Modelstropical Pacific SST
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The pith

Pre-training on climate simulations lets diffusion models recover accurate ENSO patterns from far fewer real observations than direct training needs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines whether diffusion models can learn the correct modes of tropical Pacific sea surface temperature variability, especially ENSO, despite limited observational records. Tests on synthetic data generated by Linear Inverse Models, which have known low-order structure, show that sufficient training samples allow the models to recover both Gaussian and non-Gaussian features including Eastern versus Central Pacific asymmetry. Real data such as the 700 monthly samples in ERSSTv5 fall short of the roughly 7000 samples needed for convergence, and some diffusion setups fail to capture the structure. Pre-training the model on CMIP6 simulations using a learned embedding, then fine-tuning on the scarce observations, overcomes this shortfall and matches observed statistics more closely than either Gaussian or non-Gaussian LIMs.

Core claim

Pre-training a diffusion model on CMIP6 data with a learned model embedding, followed by fine-tuning on scarce observations, reproduces observed ENSO statistics more faithfully than both Gaussian and non-Gaussian Linear Inverse Models, because the pre-training supplies enough samples for the model to learn the correct low-order structure that direct training on real data alone cannot achieve.

What carries the argument

Diffusion model with learned embedding, pre-trained on CMIP6 simulations and fine-tuned on limited observations, validated against synthetic SST fields from Linear Inverse Models with known structure.

If this is right

  • With enough training samples the diffusion model recovers the correct low-order structure of both Gaussian and non-Gaussian LIMs.
  • The 700 monthly observations in ERSSTv5 are an order of magnitude below the 7000 samples required for convergence without pre-training.
  • Not every diffusion parameterisation succeeds in recovering the correct structure even with abundant data.
  • The pre-training plus fine-tuning pipeline closes the data gap and outperforms standard LIM approaches on observed statistics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same pre-training strategy could be tested on other climate variables or regions where observational records are similarly short.
  • If the LIM proxy holds, the approach might extend to variability on longer timescales where data scarcity is even more severe.
  • The method supplies a concrete way to check whether diffusion models are capturing physically meaningful modes rather than artifacts of limited samples.

Load-bearing premise

The low-order structure recovered from LIM-generated synthetic fields is a sufficient proxy for the modes present in real tropical Pacific SST so that pre-training benefits carry over to actual observations.

What would settle it

A test showing that the pre-trained and fine-tuned diffusion model still fails to match key observed ENSO statistics, such as the Eastern/Central Pacific asymmetry, in withheld real data from ERSSTv5.

Figures

Figures reproduced from arXiv: 2606.27094 by Albert Soret, Amanda Duarte, Lluis Palma, Markus Donat, Vincent Verjans.

Figure 1
Figure 1. Figure 1: Top row (a,b,c,d,e): model trained on Linear Inverse Model (LIM) data. Bottom row (f,g,h,i,j): trained on nonlinear-Gaussian LIM (NG-LIM). Note that “true” refers to LIM￾and NG-LIM-generated data in the top and bottom row, respectively. (a,f) Scatter plots of the two leading principal components (PC1 vs PC2) for true data (green) and generated samples (grey/black), with quadratic fit curves highlighting th… view at source ↗
Figure 2
Figure 2. Figure 2: Performance of x-prediction diffusion as a function of training set size (N), eval￾uated on the NG-LIM dataset. (a) Variance-weighted PC pattern correlation. (b) Projected variance ratio. (c) Training (solid) and validation (dashed) loss. (d) Spatial skewness correlation. (e) Memorization ratio (nearest-neighbour distance of generated vs held-out to training set). Shaded bands show ±1 standard deviation ac… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of training strategies for learning the NG-LIM distribution from only N = 720 samples. (a) Variance-weighted PC pattern correlation, (b) spatial skewness correlation, (c) projected variance ratio, and (d) memorisation ratio. Strategies shown: direct training in full space (black), PCA reduction to 100D (blue), CMIP6 pre-training without fine-tuning (purple), CMIP6 pre-training with fine-tuning (… view at source ↗
Figure 4
Figure 4. Figure 4: (a–d) Scatter plots of the two dominant modes of sea surface temperature variabil￾ity (PC1 vs PC2), as generated by: (a) a linear model (LIM), (b) a non-Gaussian linear model (NG-LIM), (c) our diffusion model leveraging CMIP6 simulations and fine-tuned to ERSSTv5, and (d) the observed record (ERSSTv5, 1948–2022). (e–h) Maps of skewness—a measure of warm–cold asymmetry, where positive values (red) indicate … view at source ↗
read the original abstract

Diffusion models are increasingly applied to climate emulation, but whether they capture the correct modes of variability remains unclear, a concern amplified by data scarcity at longer timescales. We investigate this using synthetic tropical Pacific SST fields from Linear Inverse Models (LIMs), whose known low-order structure bypasses the overlapping and confounding modes of real observations. With sufficient training data, our model recovers the correct structure of both Gaussian and non-Gaussian LIMs, including ENSO's Eastern/Central Pacific asymmetry. Yet an ablation study on the number of monthly training samples reveals that the 700 observations in ERSSTv5 fall an order of magnitude short of the 7,000 samples needed for convergence, and that not all diffusion parameterisations recover the correct low-order structure. Pre-training on CMIP6 with a learned model embedding, followed by fine-tuning on scarce observations, closes this gap, reproducing observed statistics more faithfully than both Gaussian and non-Gaussian LIMs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper investigates diffusion models for emulating ENSO variability under data scarcity. Using synthetic tropical Pacific SST from Gaussian and non-Gaussian LIMs as a controlled testbed with known low-order structure, it shows that diffusion models recover the correct modes (including ENSO asymmetry) with sufficient samples (~7000), but 700 ERSSTv5 observations are insufficient. Pre-training on CMIP6 with a learned embedding followed by fine-tuning on scarce observations is shown to close the gap, yielding better reproduction of observed statistics than the LIM baselines.

Significance. If the transfer from LIM proxies to real observations holds, the approach offers a practical route to leverage large CMIP6 ensembles for improving statistical emulation of observed climate modes in data-limited regimes. The controlled LIM testbed is a clear strength, providing a falsifiable check on mode recovery before real-data application.

major comments (2)
  1. [Ablation study and real-data evaluation sections] The central claim that pre-training + fine-tuning reproduces observed ERSSTv5 statistics more faithfully than non-Gaussian LIMs rests on the untested assumption that success on LIM-generated fields implies success when the target distribution includes additional overlapping, non-stationary modes present in real tropical Pacific SST. The ablation study quantifies sample requirements only for the LIM proxy and does not include a direct comparison of embeddings learned from LIMs versus real data.
  2. [Results on ERSSTv5] The outperformance over LIM baselines on observed statistics is load-bearing for the headline result, yet the manuscript provides no quantitative metrics, error bars, or details on the exact statistics (e.g., power spectra, asymmetry measures) used for the ERSSTv5 comparison, making it impossible to assess whether the reported improvement exceeds sampling variability.
minor comments (1)
  1. [Methods] Clarify the precise architecture of the 'learned model embedding' used for pre-training and how it is transferred during fine-tuning.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive review. The comments highlight important aspects of our evaluation strategy and the need for more rigorous quantification on real data. We address each major comment below and indicate planned revisions.

read point-by-point responses

  1. Referee: The central claim that pre-training + fine-tuning reproduces observed ERSSTv5 statistics more faithfully than non-Gaussian LIMs rests on the untested assumption that success on LIM-generated fields implies success when the target distribution includes additional overlapping, non-stationary modes present in real tropical Pacific SST. The ablation study quantifies sample requirements only for the LIM proxy and does not include a direct comparison of embeddings learned from LIMs versus real data.

    Authors: We agree that the LIM testbed is a proxy and that success on synthetic data with known structure does not automatically transfer to observations containing additional non-stationary modes. The LIM experiments were designed specifically to provide a falsifiable check on whether the diffusion model can recover the correct low-order modes (including asymmetry) when the ground truth is known, which is impossible with real data. For the ERSSTv5 application, evaluation is performed by direct comparison of generated statistics against those computed from the observations themselves, rather than assuming transfer from LIM. A direct comparison of LIM-learned versus CMIP6-learned embeddings is not feasible because the true underlying modes in observations are unknown; the LIM provides the only controlled ground truth. We will add a dedicated discussion paragraph clarifying the proxy rationale, its limitations, and why embedding comparison on real data is not possible. revision: partial

  2. Referee: The outperformance over LIM baselines on observed statistics is load-bearing for the headline result, yet the manuscript provides no quantitative metrics, error bars, or details on the exact statistics (e.g., power spectra, asymmetry measures) used for the ERSSTv5 comparison, making it impossible to assess whether the reported improvement exceeds sampling variability.

    Authors: We acknowledge that the current manuscript relies on qualitative descriptions of improved reproduction of observed statistics without providing quantitative metrics or uncertainty estimates. In the revised version we will add a new table and accompanying text that reports specific quantitative comparisons (including power spectra, skewness/asymmetry measures, and variance explained by leading EOFs), with error bars obtained via bootstrap resampling of the generated ensembles. We will also explicitly list the statistics used and the procedure for assessing whether differences exceed sampling variability. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claims rest on external LIM structure and independent datasets

full rationale

The paper trains diffusion models on LIM-generated synthetic SST fields (with known low-order structure), pre-trains on CMIP6, and fine-tunes/evaluates on ERSSTv5 observations, comparing performance to Gaussian and non-Gaussian LIM baselines. No quoted equations or steps reduce a reported result to a fitted parameter on the same data, a self-definition, or a load-bearing self-citation chain. LIMs and CMIP6/ERSSTv5 serve as external references whose structure is not derived from the diffusion model itself. The ablation on sample count and the pre-training benefit are evaluated against these independent benchmarks, keeping the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that LIM-generated fields capture the relevant variability structure and that the number of samples needed for convergence (7,000) is a reliable threshold for real data. No explicit free parameters or invented entities are stated in the abstract.

axioms (1)
  • domain assumption LIMs provide a faithful low-order representation of tropical Pacific SST variability against which diffusion models can be validated
    The entire synthetic-data test bed is built on this premise; if LIMs miss important higher-order or non-stationary features, the recovery results do not transfer.

pith-pipeline@v0.9.1-grok · 5703 in / 1392 out tokens · 18262 ms · 2026-06-26T01:55:29.777793+00:00 · methodology

discussion (0)

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