Single-stage joint diffusion of sky images and clear-sky index for ultra-short-term irradiance forecasting: what the frame-to-irradiance stage discards

Kanawut Suwandee; Suwichaya Suwanwimolkul

cs.CVOct 15, 2026

Single-stage joint diffusion of sky images and clear-sky index for ultra-short-term irradiance forecasting: what the frame-to-irradiance stage discards

Authors: Kanawut Suwandee, Suwichaya Suwanwimolkul

Organizations: Chulalongkorn University, 254 Phaya Thai Rd, Wang Mai, Pathum Wan, Bangkok, 10330, Thailand

Abstract

Sky-image irradiance forecasting is dominated by a two-stage design: a video-prediction model forecasts future sky frames, and a separately trained regressor maps those frames to irradiance. We propose a single-stage alternative that co-denoises the future sky-image and clear-sky-index sequences in one diffusion process, with an irradiance head that reads a denoised preview of the future sky rather than the noised diffusion state. The forecaster needs no regression stage and runs from sky images and deterministic covariates alone, with no measured irradiance at its input --- the situation at a site with a camera but no pyranometer. On 2023 SIRTA data the model reaches a pooled RMSE of $104.1$ ~W,m $^{-2}$ and a skill score of $+0.34$ on the continuous ranked probability score (CRPS) against smart persistence, higher than any of twelve baseline configurations, and retains that skill when retrained on 2021--2022. On the model's own generated frames, a separately trained regressor reaches $150.6$ ~W,m $^{-2}$ against the joint head's $104.1$ : roughly $46$ ~W,m $^{-2}$ that joint training recovers and a cascade discards. Point accuracy is competitive but not best: a deterministic network that also reads measured irradiance attains $97.6$ ~W,m $^{-2}$ . The model's CRPS skill leads that network's in every sky-condition tertile, by $0.26$ to $0.30$ .

Figures & tables

Figure 1: \par Joint reverse diffusion: the 50-step sampling trajectory. Both streams are denoised together at every step. The fixed conditioning (green) is identical at every step. The image latents (pink) run from noise to the decoded future frames; the clear-sky-index sequence (blue) is denoised in parallel in standardised value space and converted to an irradiance forecast. The sky frames are a side output — the forecast is carried by the clear-sky-index stream. The frames shown are the ramp-up case of Figure 7 \par Effect of removing the regression stage : its eight input frames and one sample of the proposed model’s output. The noisy frames, made by adding noise to that output, and the clear-sky-index curves are illustrative. One step is expanded in Figure 3.3 \par Framework .

Figure 2: \par Inside one denoising step of the proposed model, and why the CSI denoiser reads $\hat{\bm{x\par}}_{0}$ . A single CSI denoiser is run twice. The conditioning pass emits CSI tokens, one per future frame, that enter the image denoiser’s cross-attention context undetached , alongside the time-feature token; the control image enters separately through ControlNet as additive residuals, and is not a cross-attention token. The image denoiser’s $\epsilon_{x}$ then yields $\hat{\bm{x\par}}_{0}$ , a denoised estimate of the future sky, which the prediction pass reads. Because $\hat{\bm{x\par}}_{0}$ is built from a detached $\epsilon_{x}$ , the image-to-CSI link carries forward values only: no gradient cycle closes. The four boxes on the right implement Eqs. ( Conditioning pass. ), ( Imagery pass. ), ( Imagery pass. ) and ( Prediction pass. ) in order; the conditioning pass’s provisional noise estimate $\epsilon^{\prime}_{y}$ , unused by this model, is not drawn. The candidate inputs on the left are three of the four choices in Eq. ( Design choice. ).

Arm	CSI denoiser reads	image denoiser reads	loop	$\bm{b\par}$ ?
Proposed (joint, past sky)	$\bm{e\par},\bm{y\par}_{t},\bm{a\par}$	$\bm{e\par},s_{t},\bm{a\par}^{i}$	open	no
noised state	$\bm{e\par},\bm{y\par}_{t},\bm{x\par}_{t}$	$\bm{e\par},s_{t},\bm{a\par}^{i}$	open	no
concat	$\bm{e\par},\bm{y\par}_{t},\bm{x\par}_{t},\bm{a\par}$	$\bm{e\par},s_{t},\bm{a\par}^{i}$	open	no
Proposed (joint, future sky)	$\bm{e\par},\bm{y\par}_{t},\hat{\bm{x\par}}_{0}$ ( $\bm{a\par}$ ind.)	$\bm{e\par},s_{t},\bm{a\par}^{i}$	open	no
Proposed (joint, past sky, future CSI)	$\bm{e\par},\bm{y\par}_{t},\bm{a\par}$	$\bm{e\par},s_{t},\bm{a\par}^{i},\hat{\bm{y\par}}_{0}$	open	no
Proposed (joint, future sky, future CSI)	$\bm{e\par},\bm{y\par}_{t},\hat{\bm{x\par}}_{0}$ ( $\bm{a\par}$ ind.)	$\bm{e\par},s_{t},\bm{a\par}^{i},\hat{\bm{y\par}}_{0}$	open	no

Table 1: \par What each method conditions on. Rows above the rule are arms of this work; below are the external comparators. Our arms receive no

\bm{b\par}

: the proposed model never sees a measured irradiance value. Section 8.2 \par Measured irradiance history isolates what that costs.

Method	RMSE $\downarrow$ [95% CI]	FS $\uparrow$ [95% CI]	CRPS $\downarrow$ [95% CI]	CRPSS $\uparrow$ [95% CI]
SPM	127.4 [88.7, 159.6]	–	–	–
DLinear (wo Iclr)	113.4 [83.8, 138.4]	+0.110 [+0.044, +0.144]	60.6 [45.0, 76.6]	-0.081 [-0.225, -0.004]
PatchTST (wo Iclr)	111.0 [81.4, 135.6]	+0.128 [+0.069, +0.163]	56.7 [39.8, 73.9]	-0.011 [-0.091, +0.036]
TimeXer (wo Iclr)	111.0 [81.6, 135.3]	+0.129 [+0.064, +0.166]	57.4 [40.9, 74.2]	-0.023 [-0.113, +0.029]
DLinear	109.8 [80.7, 134.2]	+0.138 [+0.079, +0.170]	58.0 [42.2, 74.2]	-0.034 [-0.156, +0.034]
PatchTST	109.6 [80.0, 133.7]	+0.140 [+0.078, +0.179]	54.5 [37.4, 72.0]	+0.029 [-0.022, +0.062]

Table 2: \par Forecast accuracy on the matched test subset (

N=1998

), with

95\%\par

day-block bootstrap intervals. RMSE and CRPS in W m -2 ; FS and CRPSS are skill scores against smart persistence, higher is better. Rules separate, from top to bottom: smart persistence; scalar forecasters without and with

I_{clr}

; the deterministic sky-image network; video predictors scored through the frozen regressor; published generative forecasters; and this work.

Figure 3: \par Forecast skill against CRPSS, every method plotted once at its headline framing. The two axes separate the comparison: SUNSET sits furthest right on point accuracy while Proposed (joint, future sky) sits highest on probabilistic skill, and no method leads on both. Methods in the lower-right quadrant beat smart persistence on the mean but not on the distribution.

	RMSE $\downarrow$ [W m -2 ]			FS $\uparrow$			CRPSS $\uparrow$
Method	in-period	cross-year	$\Delta$ $\rightarrow\!0$	in-period	cross-year	$\Delta$ $\rightarrow\!0$	in-period	cross-year	$\Delta$ $\rightarrow\!0$
SPM	127.4	–	–	—	—	—	–	–	–
PatchTST	109.6	109.0	$-0.6$	$+0.140$	$+0.145$	$+0.004$	+0.029	+0.031	$+0.002$
SUNSET	97.6	98.1	$+0.5$	$+0.234$	$+0.230$	$-0.004$	+0.060	+0.047	$-0.013$
PhyDNetGAN	112.3	110.6	$-1.8$	$+0.118$	$+0.132$	$+0.014$	-0.103	-0.073	$+0.030$
Xiong	116.9	117.2	$+0.3$	$+0.082$	$+0.080$	$-0.002$	+0.148	+0.148	$+0.000$

Table 3: \par Cross-year retraining. Methods trained on a different calendar year and evaluated on the same test set and reference as Table 5 \par Performance comparison .

\Delta

is cross-year minus in-period, computed before rounding; values near zero indicate the result does not depend on which year the model was trained on. FS is computed from the RMSE columns against the same smart-persistence reference,

127.4

W m -2 .

Figure 4: \par Performance against lead time: (a) RMSE, (b) forecast skill and (c) CRPSS, for every method in the comparison, each at its headline framing. Forecast skill and CRPSS are computed against the same smart-persistence reference as Table 5 \par Performance comparison . SkyGPT’s chunked rollout is visible as the unstable worst curve; the scalar forecasters are bracketed as one muted group.

Figure 5: \par Sky-condition tertiles on the matched test subset: the distribution of the clear-sky index

k

at the forecast origin. Dashed lines are the tertile edges,

k=0.527

and

k=1.063

, and each region holds

666

samples. The horizontal axis is cut at

k=3.2

; the

43

samples above it are binned but not shown.

	CRPSS $\uparrow$			RMSE $\downarrow$
Tertile	Proposed (joint, future sky)	SUNSET	lead	Proposed (joint, future sky)	SUNSET
Overcast	$+0.285$	$-0.002$	$+0.287$	101.6	92.6
Variable	$+0.347$	$+0.085$	$+0.262$	104.9	98.5
Clear	$+0.388$	$+0.091$	$+0.297$	105.6	101.5

Table 4: \par CRPSS and RMSE by sky-condition tertile on the matched test subset (

666

samples each), for the proposed model and SUNSET, the strongest deterministic comparator. The lead is the proposed model’s CRPSS minus SUNSET’s within the same tertile. RMSE in W m -2 . Bold marks the better method of each metric: the proposed model on CRPSS and SUNSET on RMSE, in every tertile.

	PICP90 $\uparrow$			SSR ( $\rightarrow 1.05$ )
Method	non-ramp	ramp	$\Delta$ $\rightarrow\!0$	non-ramp	ramp	$\Delta$ $\rightarrow\!0$
all deterministic methods	0.000	0.000	0	—	—	—
SkyGPT	0.235	0.236	$-0.001$	3.076	3.353	$+0.277$
Xiong	0.847	0.642	$-0.206$	0.806	1.796	$+0.990$
Proposed (joint, past sky)	0.458	0.518	$+0.060$	1.282	1.515	$+0.233$
Proposed (joint, future sky)	0.631	0.605	$-0.026$	0.972	1.227	$+0.255$

Table 5: \par Interval coverage and spread-skill ratio (SSR, Eq. ( 4.3 \par Evaluation metrics )) on ramp and non-ramp events.

\Delta

is ramp minus non-ramp; a small

\Delta

means the forecast’s reliability does not change when conditions become hard. SSR above its

1.05

target means intervals too narrow (under-dispersed), below it too wide (over-dispersed); the target is derived in Section 4.3 \par Evaluation metrics . Deterministic methods are grouped: a point forecast has zero coverage by construction and no spread to report, and is excluded from the per-column bolding. The best value in each column is in bold: highest coverage,

\Delta

closest to zero, SSR closest to the

1.05

target.

Figure 6: \par (a) Reliability of the proposed model: the nominal level

\alpha

of a central prediction interval against the empirical coverage attained at that level,

\mathrm{PICP\par}_{\alpha}

(Eq. ( 4.3 \par Evaluation metrics )), swept over nineteen levels from

0.05

0.95

; pooled (bold) and per horizon (faint). The diagonal is perfect reliability, where a nominal

\alpha

interval contains a fraction

\alpha

of the observations. (b)

\mathrm{PICP\par}_{\alpha}

\alpha=0.5

and

0.9

by sky-condition tertile; dashed lines are the nominal targets.

Panel of Figure 7 — Figure 7: \par Width of the $90\%\par$ prediction interval against ramp magnitude, one point per test sample, for (a) Proposed (joint, future sky) and (b) Xiong, on the same axes. Width is the $5$ – $95$ percentile spread of the ensemble, averaged over the eight horizons; magnitude is the largest single-step $|\Delta\mathrm{GHI\par}|$ in the forecast window. The dashed line is the $200$ W m -2 ramp threshold: the ramp subset is the region to its right. Xiong is subsampled to ten members so the two panels are comparable. Red lines are least-squares fits, of slope $0.88$ and $0.54$ .

Method	$r$ $\uparrow$	$\rho$ $\uparrow$	non-ramp	ramp	ratio
SkyGPT	$+0.657$	$+0.594$	85.4	266.0	3.1
Xiong	$+0.646$	$+0.629$	152.6	346.2	2.3
Proposed (joint, past sky)	$+0.803$	$+0.826$	61.7	355.3	5.8
Proposed (joint, future sky)	$+0.846$	$+0.822$	87.1	417.1	4.8

Table 6: \par Response of the

90\%\par

prediction interval to ramp magnitude, on the matched test subset.

r

and

\rho

are the Pearson and Spearman correlations between a sample’s mean interval width and its ramp magnitude (largest single-step

|\Delta\mathrm{GHI\par}|

); widths are means off and on the ramp subset, in W m -2 , and the ratio is their quotient. All methods at

M=10

members, Xiong subsampled to match. Deterministic methods are absent: a point forecast has no width.

Method	RMSE $\downarrow$	FS $\uparrow$	CRPSS $\uparrow$
DLinear (wo Iclr)	249.8	$+0.147$	$+0.109$
PatchTST (wo Iclr)	244.8	$+0.164$	$+0.111$
TimeXer (wo Iclr)	244.3	$+0.166$	$+0.112$
DLinear	242.3	$+0.173$	$+0.125$
PatchTST	243.3	$+0.170$	$+0.113$
TimeXer	243.3	$+0.169$	$+0.115$

Table 7: \par Forecast accuracy on the ramp subset (

n=334

of the matched test subset), scored against the same smart-persistence reference as Table 5 \par Performance comparison . RMSE in W m -2 ; FS and CRPSS are skill scores, higher is better. Rows are grouped as in Table 5 \par Performance comparison . Errors on ramps are several times their pooled values for every method, so these numbers are not comparable with Table 5 \par Performance comparison and none is quoted beside one.

Frames read	Read by	RMSE $\downarrow$ [W m -2 ]
ground-truth future frames	frozen U-Net	63.5
generated future frames	frozen U-Net	150.6
generated future frames	irradiance head of the proposed model	104.1
ground-truth future frames	irradiance head of the proposed model (oracle arm)	102.2

Table 8: \par Irradiance recovered from future sky frames by two readers, on the same

1998

samples: the frozen U-Net regressor (first two rows) and the irradiance head of the proposed model, reading its own denoised estimate of the future sky (third row) or, as the oracle arm, the true future frames (fourth row). Lower is better.

Figure 8: \par Ground-truth future frames (top row) and the frames generated by each method across the forecast horizon, for one ramp-up case. No method reproduces the ground truth closely; the relevant comparison is between the generated rows. Frame quality decreases with lead time, consistent with the per-horizon degradation of the frozen regressor reported in this section.

Figure 9: \par Measured and forecast irradiance for the same case as Figure 7 \par Effect of removing the regression stage . The shaded band is the

5

–

95\%\par

interval of the proposed model’s ten-member ensemble. The measured series rises by about

700

W m -2 between

i{+}4

and

i{+}7

; the deterministic rows follow it only partly, and the ensemble band is wide enough to contain most of the rise.

Head reads	RMSE $\downarrow$	FS $\uparrow$	CRPSS $\uparrow$
denoised estimate of future frames	104.06	+0.183	+0.341
past frames only	114.09	+0.104	+0.235

Table 9: \par Effect of the input of the irradiance head on the matched test subset, at matched training budget. Both arms have the same architecture and parameter count; only the signal read by the head differs.

Seed	control	$+$ irradiance	RMSE gain $\uparrow$	CRPSS gain $\uparrow$
1	108.51	101.45	$+7.06$	$+0.090$
2	108.13	103.37	$+4.76$	$+0.084$

Table 10: \par Conditioning the irradiance head on eight past timesteps of measured irradiance, against a matched control on the same code path. Gain is control minus stream, so positive favours the stream.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Arm	RMSE $\downarrow$	FS $\uparrow$	CRPSS $\uparrow$	SSR ( $\rightarrow 1.05$ )	imagery $\downarrow$
oracle (true future frames)	98.1	+0.207	+0.393	1.11	—
Proposed (joint, future sky)	101.8	+0.177	+0.322	1.24	152.8
Proposed (joint, past sky)	110.5	+0.107	+0.217	1.55	165.3
scalar only	107.7	+0.129	—	—	—
concat	109.0	+0.119	+0.239	1.49	182.4
noised state	113.4	+0.083	+0.234	1.01	161.1

Appendix

Table B.1 : \par Design-space survey, full 2023 test set (forecast skill against pooled

\mathrm{SPM\par}=123.7

; CRPSS against

\overline{\mathrm{MAE\par}\par}=54.01

; SSR target

1.05

; imagery via the frozen U-Net). Single seed, except Proposed (joint, future sky), a two-seed mean. Every arm here is sampled at

20

reverse diffusion steps, against the

50

used throughout the main text. The best value in each column is in bold (SSR: closest to

1.05

; ties at the printed precision are both bold); the oracle (true future frames) arm is an upper bound, not a forecast, and is excluded. Not comparable with Table 5 \par Performance comparison .

Panel of Figure 21 — Figure B.1 : \par One denoising step of Proposed (joint, future sky, future CSI). Black: the step of the proposed model, Eqs. ( Conditioning pass. )–( Prediction pass. ). Orange, dashed: what the variant adds. The conditioning pass’s noise estimate $\epsilon^{\prime}_{y}$ , detached, gives $\hat{\bm{y\par}}_{0}$ (Eq. ( How the cross-modal path works. )); inside $G_{\theta}$ , $\psi(\hat{y}^{j}_{0})$ is added to the timestep embedding $\gamma(t)$ , and the UNet call for frame $j$ reads the sum $\tilde{\gamma}^{j}(t)$ (Eq. ( How the cross-modal path works. )). Both links between the branches pass through a stop-gradient, so no gradient cycle closes. In Proposed (joint, past sky, future CSI) the prediction pass is absent: one pass reading $\bm{a\par}^{\prime}$ supplies $s_{t}$ , $\epsilon_{y}$ and, through Eq. ( How the cross-modal path works. ), $\hat{\bm{y\par}}_{0}$ .

without path	with path	$\Delta$ RMSE $\rightarrow\!0$	$\Delta$ CRPSS $\rightarrow\!0$	other differences
Proposed (joint, future sky)	Proposed (joint, future sky, future CSI)	$\phantom{-\par}0.0$	$+0.005$	selection rule; starting checkpoint
Proposed (joint, past sky)	Proposed (joint, past sky, future CSI)	$-0.2$	$+0.004$	selection rule; training budget

Appendix

Table B.2 : \par The two cross-modal comparisons.

\Delta

is with-path minus without-path, from Table Appendix B \par The wider design space ; both lie inside the noise floors of Section Run-to-run variation. . The last column lists what differs between the two arms besides the path.

Stage	Trains	Frozen	Learning rate	Stopping and checkpoint
1	VAE	—	$10^{-6}$	early stopping on validation LPIPS (patience 20)
2	UNet	VAE	$10^{-5}$ , then $10^{-6}$ for the final epochs	best validation LPIPS (patience 20)
3	ControlNet	VAE, UNet	$10^{-5}$ , cosine schedule	best validation LPIPS (patience 20)
4	Joint diffusion training (phase 1): image tokenizer, CSI denoiser, temporal refiner	VAE, UNet, ControlNet	$10^{-4}$	19–20 epochs; best validation LPIPS $+$ CSI RMSE
5	Joint diffusion training (phase 2): all except the VAE	VAE	$10^{-6}$ , halved on plateau	at most 31 epochs; best validation LPIPS $+$ CSI RMSE

Appendix

Table C.1 : \par The five training stages: three image-side stages, then joint diffusion training in two phases. Each stage starts from the checkpoint the previous one selected. Validation criteria are computed on the validation split (Section 4 \par Data and experimental setup ).

	frozen regressor on				$\Delta$ FS, cross-year
Horizon	true frames	generated	CRPSS	$\mathrm{PICP\par}_{90}$	Proposed (joint, future sky)	SUNSET
i+1	65.7	142.9	$+0.034$	0.660	$+0.015$	$+0.004$
i+2	61.3	144.2	$+0.252$	0.615	$+0.018$	$+0.006$
i+3	63.8	145.3	$+0.325$	0.634	$+0.022$	$+0.005$
i+4	63.1	146.9	$+0.375$	0.600	$-0.027$	$-0.001$
i+5	65.3	151.7	$+0.410$	0.623	$-0.008$	$+0.004$

Appendix

Table C.2 : \par Per-horizon values behind statements made as ranges in the main text: the frozen U-Net regressor applied to the ground-truth and to the generated future frames (RMSE, W m -2 , Section 7 \par Effect of removing the regression stage ); the CRPSS of Proposed (joint, future sky) (Section 6.1 \par Per-horizon performance ); its empirical coverage at the nominal

90\%\par

level,

\mathrm{PICP\par}_{90}

(Section 6.3 \par Reliability of the predictive intervals ); and the cross-year minus in-period forecast skill of Proposed (joint, future sky) and SUNSET (Section 5.1 \par Cross-year performance ). Matched test subset,

50

sampling steps.

	RMSE $\downarrow$			CRPSS $\uparrow$
Method	all	contiguous	QC-valid	all	contiguous	QC-valid
SPM	127.4	127.8	128.7	–	–	–
DLinear (wo Iclr)	113.4	113.8	114.2	$-0.081$	$-0.081$	$-0.074$
PatchTST (wo Iclr)	111.0	111.4	111.9	$-0.011$	$-0.010$	$-0.008$
TimeXer (wo Iclr)	111.0	111.4	111.8	$-0.023$	$-0.023$	$-0.019$
DLinear	109.8	110.1	110.6	$-0.034$	$-0.035$	$-0.033$

Appendix

Table C.3 : \par Point estimates on the matched test subset with all

1998

windows, without the

13

that are not contiguous (contiguous,

N=1985

), and without the

62

whose targets or persistence origin include a minute SIRTA has since marked unusable (QC-valid,

N=1936

); Section 4.1 \par Dataset . RMSE in W m -2 ; CRPSS against smart persistence on the same windows. The best value in each column is in bold. No method changes rank on either score in either comparison, and none of the

13

non-contiguous windows is in the ramp-event subset of Section 6.4 \par Ramp events .

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Accurate solar irradiance forecasting is essential for the reliable integration of photovoltaic power into modern electricity grids. All-sky imagers (ASI) provide high-resolution observations of clouds, making them well suited for intra-hour forecasting. Recent deep learning approaches have substantially improved forecast accuracy but are often limited by deterministic predictions and a reduced capability to anticipate ramp events. This work proposes FarSky, a generative forecasting framework that leverages latent-space coupling to learn task-aware representations of sky images. A multi-task autoencoder first learns a shared latent representation for image reconstruction and irradiance estimation. A latent diffusion model then generates future latent states conditioned on recent observations, from which irradiance forecasts are directly decoded. Probabilistic forecasts are inherently obtained through stochastic sampling. The framework is developed using a multi-year ASI dataset acquired at the Plataforma Solar de Almería, Spain, and evaluated on two independent test datasets against persistence, state-of-the-art end-to-end, and generative forecasting approaches. FarSky achieves the best overall deterministic and probabilistic forecasting performance, improving forecast skill by up to 11 percentage points. Furthermore, it substantially improves ramp event detection over existing methods, achieving F1-scores above 60%. These results demonstrate the potential of combining generative models with task-aware latent-space coupling for solar forecasting.

Abstract

Solar Irradiance Forecasting

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