Paper deep dive
NowcastDiT: Diffusion Transformers are Effective Precipitation Nowcasters
Haoran Xu, Xingzhuo Guo, Yuchen Zhang, Jincheng Zhong, Jianmin Wang, Mingsheng Long
Intelligence
Status: not_run | Model: - | Prompt: - | Confidence: 0%
Entities (0)
Relation Signals (0)
No relation signals yet.
Cypher Suggestions (0)
No Cypher suggestions yet.
Abstract
Abstract:Precipitation nowcasting demands accurate short-term forecasts under strong spatiotemporal variability. Diffusion models are well suited to modeling complex precipitation distributions, yet existing approaches often introduce increasingly specialized designs, leaving the capability of a standard diffusion architecture underexplored. We show that a standard Diffusion Transformer already provides a simple and scalable foundation for precipitation nowcasting, with domain-specific requirements accommodated naturally within its design space. Based on this principle, we develop NowcastDiT and instantiate this flexibility through two complementary adaptations: a dynamics-aware noise prior for temporally coherent forecasts, and end-to-end reinforcement learning with timestep-aware rewards for meteorological skill. Experiments on SEVIR and MRMS benchmarks show that NowcastDiT achieves state-of-the-art performance in both perceptual quality and meteorological skill. These results suggest that standard DiT can serve as an effective foundation for precipitation nowcasting.
Tags
Links
- Source: https://arxiv.org/abs/2609.37038v1
- Canonical: https://arxiv.org/abs/2609.37038v1
Trouble viewing inline? Open PDF directly →
Full Text
85,554 characters extracted from source content.
Expand or collapse full text
NowcastDiT: Diffusion Transformers are Effective Precipitation Nowcasters Haoran Xu †thanks: Equal contribution. 🖂 Corresponding author. Affiliation: School of Software, BNRist, Tsinghua University, China Email: xuhaoran26@mails.tsinghua.edu.cn Xingzhuo Guo11footnotemark: 1 Affiliation: School of Software, BNRist, Tsinghua University, China Email: gxz23@mails.tsinghua.edu.cn Yuchen Zhang Affiliation: Envision Energy, China Email: mingsheng@tsinghua.edu.cn Jincheng Zhong Affiliation: Kling Team, Kuaishou Technology, China Jianmin Wang Affiliation: School of Software, BNRist, Tsinghua University, China Mingsheng Long Affiliation: School of Software, BNRist, Tsinghua University, China Abstract Precipitation nowcasting demands accurate short-term forecasts under strong spatiotemporal variability. Diffusion models are well suited to modeling complex precipitation distributions, yet existing approaches often introduce increasingly specialized designs, leaving the capability of a standard diffusion architecture underexplored. We show that a standard Diffusion Transformer already provides a simple and scalable foundation for precipitation nowcasting, with domain-specific requirements accommodated naturally within its design space. Based on this principle, we develop NowcastDiT and instantiate this flexibility through two complementary adaptations: a dynamics-aware noise prior for temporally coherent forecasts, and end-to-end reinforcement learning with timestep-aware rewards for meteorological skill. Experiments on SEVIR and MRMS benchmarks show that NowcastDiT achieves state-of-the-art performance in both perceptual quality and meteorological skill. These results suggest that standard DiT can serve as an effective foundation for precipitation nowcasting. 1 Introduction Precipitation nowcasting aims to predict the short-term evolution of rainfall fields at high spatial and temporal resolutions. An effective forecasting system is expected to accurately capture complex spatiotemporal dynamics, account for intrinsic uncertainty, and maintain reliability for rare but high-impact precipitation events (Wang et al., 2017). From a generative modeling perspective, precipitation nowcasting is fundamentally a conditional generation task, with diffusion models (Ho et al., 2020; Song et al., 2021; Lipman et al., 2023) providing a natural framework given their strong capability for probabilistic image and video generation(Peebles and Xie, 2023; Wan et al., 2025; Seedance et al., 2026; Aditi et al., 2026). Beyond these general modeling capabilities, existing works have focused on several precipitation-specific requirements, particularly temporal coherence across forecast frames and meteorological skill in capturing high-impact events. To address them, existing generative methods introduce various task-specific designs including physics-based motion constraints (Zhang et al., 2023), intensity continuity regularization (Gao et al., 2023), and decomposition-based modeling frameworks (Yu et al., 2024; Gong et al., 2024; Wen et al., 2026). Despite their different forms, these methods follow a common design philosophy: specializing the generative framework to explicitly encoding these requirements. While effective, this line of development narrows the exploration of foundational model designs for precipitation nowcasting, leaving a more fundamental question insufficiently explored: how necessary is task-specific specialization beyond a standard diffusion model? Figure 1: Comparison of diffusion modeling paradigms for precipitation nowcasting. (a): Specialized diffusion nowcasters encode domain knowledge through task-specific models or losses. (b): A standard DiT is applicable for precipitation nowcasting. (c): NowcastDiT adds minimal precipitation-specific adaptation towards a standard DiT without changing its backbone. In this paper, we argue that a standard Diffusion Transformer provides a sufficient foundation for precipitation nowcasting. We posit that precipitation nowcasting is not fundamentally different from conditional video generation in terms of its core generative modeling requirements, as both require capturing complex spatiotemporal dynamics under uncertainty, capabilities that have already been demonstrated by modern video diffusion models (Seedance et al., 2026; Aditi et al., 2026). Meanwhile, precipitation-specific requirements can be accommodated within the broader design space of diffusion models, as suggested by the versatility of modern diffusion models across diverse video generation tasks (Guo et al., 2025; Xue et al., 2025) To this end, we propose the Nowcasting Diffusion Transformer (NowcastDiT), a simple and scalable framework built on a standard DiT with minimal precipitation-specific adaptations. From the diffusion perspective, NowcastDiT introduces a dynamics-aware noise prior that captures shared evolution patterns and variations across forecast frames to enforce temporal coherence. From the training perspective, NowcastDiT incorporates end-to-end reinforcement learning with timestep-aware rewards to enhance meteorological skill. On two widely recognized radar-based benchmarks, SEVIR and MRMS, NowcastDiT achieves state-of-the-art performance across both perceptual quality and meteorological skill metrics. These results suggest that standard DiT can serve as an effective foundation for precipitation nowcasting. Our contributions are summarized as follows: • We revisit precipitation nowcasting from the perspective of standard diffusion models, and show that a standard DiT provides a sufficient foundation, with precipitation-specific requirements handled through targeted adaptation rather than model specialization. • Based on this principle, we propose NowcastDiT, a simple and scalable framework that retains the standard DiT with a dynamics-aware noise prior to promote temporal coherence and reinforcement learning with timestep-aware rewards to enhance meteorological skill. • Extensive experiments on SEVIR and MRMS demonstrate the state-of-the-art performance of NowcastDiT, validating standard DiT as an effective foundation for precipitation nowcasting. 2 Preliminaries Precipitation nowcasting aims to predict S future frames 1:Sx^1:S from past frames −S0:0x^-S_0:0. Following Rombach et al. (2022), we first train a VAE with encoder E and decoder D, then generate 1=E(S)z_1=E(x^S) conditioned on =E(−S0:0)c=E(x^-S_0:0) within the latent space. Diffusion models learn to denoise noise-corrupted data through simple linear interpolation, learning a conditional velocity field with the flow-matching objective: t=(1−t)ϵ+t1, _t=(1-t) ε+tz_1, (1) ℒFM(θ) _FM(θ) =1,,ϵ,t[‖θ(t,t∣)−(1−ϵ)‖22], =E_z_1,c, ε,t [ \|v_θ(z_t,t )-(z_1- ε) \|_2^2 ], (2) where t∈[0,1]t∈[0,1] denotes the diffusion timestep and ϵ∼(,) ε (0,I) is Gaussian noise. At inference, we solve dtdt=θ(t,t∣) dz_tdt=v_θ(z_t,t ) from 0=ϵz_0= ε to ^1 z_1 and decode ^1:S=D(^1) x^1:S=D( z_1). 3 Revisiting Precipitation Nowcasting Requirements In this section, we revisit the modeling requirements of precipitation nowcasting and ask whether they necessitate specialized forecasting architectures. We organize the discussion around three aspects: spatiotemporal generative modeling, physical plausibility, and precipitation alignment. Spatiotemporal generative modeling. Precipitation fields, like natural videos, are continuous spatiotemporal tensors whose structures span multiple scales, from localized convective cells to large-scale frontal systems. A suitable model must capture these hierarchical dependencies while representing the uncertainty of future evolution. The success of DiTs in video generation (OpenAI, 2024; Wan et al., 2025; Seedance et al., 2026) suggest that their scalable spatiotemporal representations provides a suitable foundation for this purpose. Physical plausibility. Precipitation evolves through atmospheric processes, and plausible forecasts should exhibit consistent motion and physically reasonable temporal evolution. Explicit physical constraints offer one way to encourage such behavior, but they are not the only route. Modern generative models have demonstrated the ability to learn intuitive physics from video (Ali et al., 2025; Ye et al., 2026; Aditi et al., 2026), suggesting that data-driven DiTs can also capture the coherent motion and local evolution from radar sequences. Precipitation alignment. Precipitation differs from natural video mainly in its data distribution and task objectives. Its evolution combines large-scale advection with localized growth and decay, with precipitation intensities commonly sparse and long-tailed. Moreover, generic generative objectives do not directly optimize meteorological skills such as Critical Success Index (CSI) and Heidke Skill Score (HSS). These discrepancies therefore call for precipitation-aware adaptation of the generative process and learning objective, but do not by themselves prescribe a specialized model or alter the underlying spatiotemporal modeling problem. Existing nowcasting methods often couple such domain-specific mechanisms with specialized forecasting models or frameworks. This coupling obscures how much task-specific specialization is genuinely needed beyond the capabilities of a general-purpose generative model. The analysis above suggests a cleaner separation: retain a standard DiT for general spatiotemporal modeling, and introduce specialization only where precipitation departs from generic generation. Takeaway. A standard DiT provides the core modeling capacity required for precipitation nowcasting, while precipitation-specific requirements can be addressed through targeted adaptations rather than model re-design. 4 NowcastDiT In this section, we present NowcastDiT, a precipitation nowcasting framework built on a standard Diffusion Transformer with minimal modifications. As illustrated in Figure 2, it promotes temporal coherence through scheduled noise correlation and meteorological skill through timestep-aware rewards, framing precipitation nowcasting as a natural extension of video diffusion modeling. Figure 2: Overview of NowcastDiT. Left: A standard Diffusion Transformer predicts future precipitation conditioned on encoded observations, with QK-Norm and 3D RoPE. Top right: The dynamics-aware noise prior (DyPro) schedules cross-frame noise correlation from temporally correlated at the noise endpoint to independent at the clean endpoint. Bottom right: Timestep-aware post-training shifts the reward emphasis from structure to detail along the denoising trajectory. 4.1 Transformer Backbone Precipitation nowcasting shares the core spatiotemporal modeling requirements of video generation, making a standard diffusion transformer a natural backbone. Following standard visual-conditioning designs in video diffusion models (Blattmann et al., 2023a; Blattmann et al., 2023b; Voleti et al., 2022; Gupta et al., 2024), NowcastDiT conditions future latent generation on historical observations by adding encoded observations to the noisy patch embeddings. One advantage of preserving a task-agnostic backbone is that NowcastDiT can inherit advances from broader generative modeling. Specifically, we incorporate two such advances that directly address the modeling requirements of precipitation nowcasting. QK-Norm. Radar-based precipitation observations yield a sparse, long-tailed intensity distribution, which can produce large variations in token feature magnitudes and attention logits. To keep attention computation well scaled during optimization, we apply QK-Norm (Henry et al., 2020) to normalize query and key vectors before their dot product. 3D RoPE. Precipitation sequences form a regular spatiotemporal grid, and their evolution is characterized by relative displacement across frames and spatial locations. Following CogVideoX (Yang et al., 2024) and Wan (Wan et al., 2025), we apply RoPE (Su et al., 2024) along the temporal, height, and width axes, enabling attention to encode relative offsets along all three dimensions in spacetime. Overall, NowcastDiT retains a deliberately simple framework: it relies on a standard DiT without task-specialized forecasting modules, explicit physical constraints, or cascaded architectures. 4.2 Temporal Coherence with Scheduled Noise Correlation Standard video diffusion formulations typically adopt i.i.d. Gaussian noise over the spatiotemporal volume, yielding independent noise realizations across forecast frames. While simple and broadly applicable, this frame-wise independence is less aligned with the strong temporal coherence inherent in precipitation evolution. Dynamics-aware noise prior. Existing approaches that adapt pretrained image diffusion models for video generation have shown that correlating noise across adjacent forecast frames can improve temporal consistency (Ge et al., 2023; Chang et al., 2024). Motivated by this insight, we introduce a dynamics-aware noise prior (DyPro) that correlates noise across forecast frames. To construct this prior, we draw on the progressive noise schedule following Dynamical Diffusion (Guo et al., 2025), with the strength of cross-frame correlation controlled by diffusion timestep. Let s∈1,…,Ss∈\1,…,S\ index the forecast frames, and let ϵ1:St ε^1:S_t denote the corresponding noise sequence at timestep t. For a fixed diffusion timestep t, DyPro recursively constructs ϵt1=1,ϵts=γtϵts−1+1−γts. ε^1_t= ξ^1, ε^s_t= _t ε^s-1_t+ 1- _t\, ξ^s. (3) Here, s∼(,) ξ^s (0,I) are independent Gaussian samples, and the diffusion-timestep-dependent inheritance weight is γt=α2(1−t)21+α2(1−t)2, _t= α^2(1-t)^21+α^2(1-t)^2, (4) where hyperparameter α≥0α≥ 0 controls the temporal dependence together with t. The recursion preserves the standard Gaussian marginal of each frame, ϵts∼(,) ε^s_t (0,I), while modifying only the cross-frame covariance. Specifically, for two frames k steps apart, Cov(ϵts,ϵts−k)=γtk/2Cov( ε^s_t, ε^s-k_t)= _t^k/2I. Thus, adjacent frames share the most similar noise, and this similarity decays geometrically with temporal distance k. As denoising proceeds, γt _t decreases from α2/(1+α2)α^2/(1+α^2) at the beginning to zero at the clean endpoint. DyPro therefore promotes spatiotemporal coherence over the fixed radar grid during early denoising, while progressively relaxing the coupling during later stages to preserve variations among individual forecast frames associated with localized precipitation growth, decay, and intensity evolution. Algorithm 1 DyPro Training ⬇ # x: training latents; c: history # net(z, t, c): predicts x - e t = sample_t() # Construct time-dependent noise e_init = randn_like(x) e = correlate(e_init, t) z = t * x + (1 - t) * e v = x - e v_pred = net(z, t, c) loss = l2_loss(v - v_pred) update(net, loss) Algorithm 2 DyPro Sampling (w/o CFG) ⬇ # c: history; shape: latent shape # N: number of sampling steps ts = linspace(0, 1, N + 1) z = correlate(randn(shape), 0) for t, t_next in zip(ts[:-1], ts[1:]): v = net(z, t, c) x = z + (1 - t) * v e = z - t * v e_init = decorrelate(e, t) e = correlate(e_init, t_next) z = t_next * x + (1 - t_next) * e return z Training and Inference. DyPro is independent of the backbone, preserving the model’s input and output shapes and the form of the training objective. During training, we use DyPro noise to construct tz_t and the flow-matching target (Algorithm 1). At inference, we use a sampler following Dynamical Diffusion that updates noise correlation at each step (Algorithm 2). The sampler requires one network evaluation per step, matching standard Euler sampling in styles. 4.3 Meteorological Skill with Timestep-Aware Rewards Standard generative models are typically optimized with surrogate objectives such as flow matching and evaluated by metrics aligned with generative fidelity. Yet precipitation nowcasting also emphasizes task-specific meteorological skill that does not necessarily align with these objectives, making flow matching alone insufficient for optimizing forecasting performance. Existing work has shown that task-specific evaluation metrics can serve directly as verifiable rewards for optimizing generative prediction models (Wu et al., 2025; Xue et al., 2025). Inspired by the pretraining–posttraining paradigm of foundation models, we adopt a two-stage training strategy that separates general generative modeling from meteorological skill optimization: • Stage 1: Pretrain a diffusion model from scratch with surrogate flow matching objective. • Stage 2: Posttrain the diffusion model by directly optimizing meteorological skills. Skill optimization via GRPO. We formulate the posttraining stage as a GRPO objective for diffusion models (Shao et al., 2024; Liu et al., 2025). For each conditioning context paired with a ground-truth future sequence ∗x^*, we sample a group of forecasts ^(1),^(2),…,^(G)\ x^(1), x^(2),…, x^(G)\ through a sampling trajectory where selected ODE transitions are converted into SDE transitions that serve as stochastic policy actions with tractable likelihoods, following the design of MixGRPO (Li et al., 2025). We score each ^(i) x^(i) against ∗x^* and update the stochastic transitions using the clipped group-relative objective A^ni A_n^i =R(^(i),∗,tn)−mean(R(^(j),∗,tn)j=1G)std(R(^(j),∗,tn)j=1G), = R( x^(i),x^*;t_n)- *mean ( \R( x^(j),x^*;t_n) \_j=1^G )std ( \R( x^(j),x^*;t_n) \_j=1^G ), (5) GRPO(θ)=1G|ℓ|∑n∈ℓ∑i=1Gmin(ρni(θ)A^ni,clip(ρni(θ),1−ε,1+ε)A^ni), _GRPO(θ)= 1G|W_ | _n _ _i=1^G ( _n^i(θ) A_n^i,clip\! ( _n^i(θ),1- ,1+ ) A_n^i ), (6) where R denotes the reward evaluated on the final forecast, ℓW_ indexes the stochastic transitions included in the GRPO update, and ρni _n^i is the policy likelihood ratio for forecast i at transition n. Further details on GRPO optimization and mixed ODE–SDE sampling are provided in Appendix C.3 and Appendix C.1, respectively. Timestep-aware rewards. Reinforcement learning for diffusion models typically uses the same terminal reward across all denoising transitions. However, different denoising transitions are expected to contribute differently to the final forecast: transitions near the noise endpoint establish precipitation coverage and large-scale spatial patterns, whereas transitions near the clean endpoint refine local intensity variations and heavy-precipitation cores. This uniform supervision may therefore be suboptimal. We introduce a timestep-aware terminal reward that gradually shifts its emphasis from precipitation structure to local detail as denoising proceeds: Rnoise(^,∗) R_noise( x,x^*) =∑τ∈lowλτCSIτpool(^,∗)+λsSSIM(^,∗), = _τ _low _τCSI^pool_τ( x,x^*)+ _sSSIM( x,x^*), (7) Rclean(^,∗) R_clean( x,x^*) =∑τ∈highλτCSIτ(^,∗)−λpLPIPS(^,∗), = _τ _high _τCSI_τ( x,x^*)- _pLPIPS( x,x^*), (8) R(^,∗,t) R( x,x^*;t) =(1−t)Rnoise(^,∗)+tRclean(^,∗), =(1-t)R_noise( x,x^*)+tR_clean( x,x^*), (9) where lowT_low and highT_high denote the light-precipitation and heavy-precipitation threshold sets, respectively. The coefficients λs _s and λp _p balance the constituent metrics, while the remaining weight is distributed uniformly across the corresponding CSI thresholds: λτ=(1−λs)/|low| _τ=(1- _s)/|T_low| for RnoiseR_noise and λτ=(1−λp)/|high| _τ=(1- _p)/|T_high| for RcleanR_clean. We empirically set λs=0.5 _s=0.5 and λp=0.9 _p=0.9. Specifically, RnoiseR_noise combines spatially tolerant low-threshold pooled CSI for event coverage with SSIM (Wang et al., 2004) for local structural agreement, while RcleanR_clean combines high-threshold CSI for localized intense precipitation with negative LPIPS (Zhang et al., 2018) for perceptual similarity in deep feature space. Since t=0t=0 and t=1t=1 correspond to the noise and clean endpoints, respectively, the reward gradually shifts from RnoiseR_noise to RcleanR_clean, emphasizing precipitation structure early and local detail later. All rewards are computed on the final decoded forecast, with the active transition time determining the metric mixture used for credit assignment in Equation 5. 5 Experiments Table 1: Performance comparison on SEVIR and MRMS. ↑ indicates higher is better and ↓ indicates lower is better. Bold and underlined values denote the best and second-best results, respectively. SEVIR MRMS Method CSI↑ CSI↑181_181 CSI↑219_219 HSS↑ LPIPS↓ SSIM↑ Method CSI↑ CSI↑16_16 CSI↑32_32 HSS↑ LPIPS↓ SSIM↑ ConvLSTM 0.2912 0.0684 0.0336 0.3571 0.2989 0.7257 ConvLSTM 0.2159 0.0514 0.0172 0.2877 0.3013 0.8978 PhyDNet 0.2874 0.0664 0.0211 0.3523 0.3081 0.7252 PhyDNet 0.2332 0.0635 0.0268 0.3111 0.3005 0.9001 Earthformer 0.2752 0.0496 0.0213 0.3391 0.3376 0.7142 Earthformer 0.2353 0.0691 0.0297 0.3152 0.3001 0.8994 SimVP 0.2951 0.0753 0.0416 0.3630 0.3113 0.7247 SimVP 0.2366 0.0657 0.0277 0.3155 0.2992 0.9006 AlphaPre 0.2980 0.0860 0.0436 0.3677 0.2897 0.7301 AlphaPre 0.2309 0.0587 0.0211 0.2933 0.3014 0.8944 DiffCast 0.2977 0.0915 0.0571 0.4033 0.1812 0.6774 NowcastNet 0.2244 0.1145 0.0729 0.3083 0.2007 0.8502 PreDiff 0.2859 0.0893 0.0487 0.3647 0.1543 0.7006 PreDiff 0.2283 0.1083 0.0695 0.3148 0.1906 0.8633 CasCast 0.2905 0.0930 0.0503 0.3703 0.1583 0.7012 CasCast 0.2224 0.0925 0.0527 0.3064 0.2045 0.8791 DiT 0.2926 0.0948 0.0555 0.3733 0.1545 0.7048 DiT 0.2343 0.1015 0.0611 0.3223 0.1953 0.8824 NowcastDiT 0.3240 0.1241 0.0750 0.4148 0.1469 0.7197 NowcastDiT 0.2696 0.1373 0.0958 0.3668 0.1827 0.8642 We evaluate NowcastDiT on two radar-based benchmarks, SEVIR and MRMS. Comparisons with deterministic and generative nowcasting baselines assess both meteorological skill and perceptual quality. Additional experiments examine how our design choices affect forecasting performance. 5.1 Experimental Setup Figure 3: Qualitative comparison on SEVIR. Forecasts are shown every 10 minutes up to 100 minutes. Colors indicate VIL values. Datasets. SEVIR (Veillette et al., 2020) is a spatiotemporal radar observation dataset covering weather events across the United States. Following prior work (Yu et al., 2024; Lin et al., 2025), we use Vertically Integrated Liquid (VIL) observations at a 5-minute temporal resolution to predict 20 future frames given 5 observed frames at 128×128128× 128 resolution. MRMS (Zhang et al., 2016) is a composite radar dataset collected over the contiguous United States. Following NowcastNet (Zhang et al., 2023), we use precipitation-rate observations at a 10-minute temporal resolution to predict 20 future frames given 4 observed frames at 256×256256× 256 resolution. Additional dataset details, splits, and preprocessing are provided in Appendix D.1. Evaluation. We compare NowcastDiT with deterministic and generative methods. The deterministic baselines include ConvLSTM (Shi et al., 2015), PhyDNet (Guen and Thome, 2020), Earthformer (Gao et al., 2022b), SimVP (Gao et al., 2022a), and AlphaPre (Lin et al., 2025), while the generative baselines include NowcastNet (Zhang et al., 2023), PreDiff (Gao et al., 2023), DiffCast (Yu et al., 2024), and CasCast (Gong et al., 2024). We evaluate meteorological skill using the Critical Success Index (CSI) (Schaefer, 1990) and Heidke Skill Score (HSS) (Jolliffe and Stephenson, 2012), and perceptual quality using the Structural Similarity Index (SSIM) (Wang et al., 2004) and Learned Perceptual Image Patch Similarity (LPIPS) (Zhang et al., 2018). CSI measures event detection accuracy, while HSS accounts for agreement expected by chance. Both are computed from pixelwise contingency counts aggregated over the evaluation set at each forecast lead time. We report their means over lead times and thresholds, using 16,74,133,160,181,219\16,74,133,160,181,219\ in the VIL for SEVIR and 1,2,4,8,16,32\1,2,4,8,16,32\ m h-1 for MRMS. We additionally report high-threshold CSI to assess intense precipitation events. SSIM measures local structural agreement, whereas LPIPS measures perceptual distance in deep feature space. Higher CSI, HSS, and SSIM and lower LPIPS indicate better performance. Metric definitions are provided in Appendix D.2. Implementation Details. We train NowcastDiT using AdamW with (β1,β2)=(0.9,0.95)( _1, _2)=(0.9,0.95), a batch size of 32, and learning rates of 10−410^-4 for pretraining and 10−510^-5 for post-training. The default backbone has 12 Transformer blocks, a hidden dimension of 768, and 12 attention heads. The DyPro parameter α is set to 0.5. Post-training uses a group size of 16, 10 denoising steps, an SDE window size of 4, and a policy ratio clipping range of 10−410^-4. For reward computation, we apply 4×44× 4 max pooling to low-threshold CSI and set the SSIM and LPIPS mixing weights to 0.5 and 0.9, respectively. All training runs use four NVIDIA A100 GPUs with 80 GB of memory each. Additional post-training settings are provided in Appendix C.6. 5.2 Main Results We compare NowcastDiT with deterministic and generative nowcasting methods on SEVIR and MRMS, reported in Table 1. The standard DiT baseline already achieves competitive performance against specialized nowcasting models, demonstrating the strength of its general-purpose spatiotemporal modeling. Relative to the strongest baselines, NowcastDiT improves aggregate CSI by 8.7% and 15.1%, and HSS by 2.9% and 13.8%, on SEVIR and MRMS, respectively. It also reduces LPIPS by 4.8% and 4.1% while achieving the best SSIM among generative methods on SEVIR. On high-threshold CSI that directly reflects the ability to detect rare and operationally important intense rainfall events, NowcastDiT achieves relative gains of 19.9%–31.4% across the reported high thresholds, showing a clear advantage in heavy-rainfall prediction. We also provide per-lead-time CSI and HSS curves, shown in Appendix E.1. Taken together, these results show that a standard DiT, with precipitation-specific alignment can achieve strong nowcasting performance while retaining a simple architecture. Figure 4: Qualitative comparison on MRMS. Forecasts are shown every 20 minutes up to 200 minutes. Colors indicate precipitation rate in m h-1. Qualitative comparisons. Figures 3 and 4 compare forecast sequences on SEVIR and MRMS, respectively. In the SEVIR example, NowcastDiT retains localized high-intensity regions at longer lead times, whereas the DiT baseline produces smoother precipitation fields. In the MRMS example, NowcastDiT better preserves the shape of the main rainband. These selected examples complement the test-set comparisons in Table 1. 5.3 Analyses We analyze how the following components and design choices affect model performance on SEVIR. Model parameter scaling. Diffusion Transformer is validated as a scalable backbone, and we investigate whether this scaling benefits extend to precipitation nowcasting. Following Peebles and Xie (2023), we evaluate NowcastDiT across a range of model sizes. As shown in Figure 5(a), increasing model size consistently improves aggregate CSI. This finding supports model scaling as an effective strategy for strengthening the forecasting capabilities of a standard DiT backbone, which forms the initial motivation of NowcastDiT. CFG and skill-aware post-training. Classifier-free guidance (CFG) (Ho and Salimans, 2022) is a common capability of standard diffusion models and should be naturally inherited when adopting them for precipitation nowcasting. We therefore examine whether skill-aware post-training can provide complementary gains on top of CFG, whose integration with diffusion post-training is not always trivial (Zheng et al., 2026). As shown in Figure 5(b), both CFG and RL improve aggregate CSI over the base model, and their combination achieves the best performance. This suggests that meteorological alignment provides an additional optimization axis beyond standard diffusion guidance. Detailed methods and results are provided in Appendix E.3. DyPro correlation strength. For simplicity, NowcastDiT adopts the factor α=0.5α=0.5 controlling temporal correlations in DyPro. To assess the senstivity, we vary the DyPro correlation strength α∈0,0.25,0.33,0.66,0.75α∈\0,0.25,0.33,0.66,0.75\, where α=0α=0 infers the i.i.d. noise baseline. Figure 5(c) shows that all tested nonzero strengths improve aggregate CSI, with performance peaking at a moderate strength and declining as the correlation increases further, indicating the robustness of α in DyPro. Detailed results are provided in Appendix E.4. Timestep-aware reward. The reinforcement learning stage of NowcastDiT uses a stage-aware reward to account for the different roles of reward metrics near the noise and clean endpoints. We compare it with a static baseline that mixes the same rewards without timestep-dependent weighting. As shown in Figure 5(d), timestep-aware weighting consistently performs better. To isolate this effect, we further repeat the comparison under CSI-only and perceptual-only objectives (i.e., λs=λp=0 _s= _p=0 and λτ=0 _τ=0, respectively), where the same trend holds. These results confirm the benefit of timestep-aware weighting across reward objectives, while mixed metrics provide a better balance between meteorological skill and perceptual quality. Figure 5: Analysis on SEVIR. Bar lengths indicate CSI gains relative to the first setting in each panel; labels report absolute CSI values. 6 Related Work Diffusion models for precipitation nowcasting. Diffusion models have become an important paradigm for probabilistic nowcasting due to their stable training dynamics and strong generative fidelity (Gao et al., 2023; Yu et al., 2024). Existing diffusion-based approaches often incorporate task-specific mechanisms to improve meteorological applicability (Gao et al., 2023; Yu et al., 2024; Gong et al., 2024; Wen et al., 2026). PreDiff (Gao et al., 2023) introduces intensity continuity guidance over a spatiotemporal architecture to strength physical alignment. DiffCast (Yu et al., 2024) introduces decomposited training phases for the modeling of global deterministic motion and local stocastic variations. CasCast (Gong et al., 2024) employs a cascaded DiT framework in latent space to decouple deterministic and stochastic precipitation modeling for improved efficiency and extreme event fidelity. These approaches couple domain-specific mechanisms with architectural and framework design, leaving unresolved whether specialized designs are necessary for effective precipitation nowcasting. In contrast, NowcastDiT examines how a standard DiT can support effective nowcasting and address domain-specific requirements within its design space. Advances in generative modeling techniques. Recent advances in image and video generation have substantially broadened the modeling capabilities of diffusion transformers (Peebles and Xie, 2023; Esser et al., 2024; Ma et al., 2025; Wan et al., 2025). Architectural refinements improve attention stability and positional modeling (Henry et al., 2020; Su et al., 2024; Gupta et al., 2024; Yang et al., 2024). Noise-prior designs introduce temporal dependencies to promote coherent video generation (Ge et al., 2023; Chang et al., 2024; Guo et al., 2025). Post-training strategies align generated outputs with task-specific objectives through reinforcement learning (Black et al., 2024; Liu et al., 2025; Xue et al., 2025; Li et al., 2025; Wu et al., 2025). Together, these developments establish the feasibility of meeting domain-specific modeling requirements within the design space of a standard DiT. Building on this foundation, NowcastDiT further develops noise-prior and post-training designs to model precipitation dynamics and enhance meteorological skill. 7 Conclusion This work demonstrates that a standard Diffusion Transformer, with targeted adaptations to its diffusion and training strategies, is sufficient for effective precipitation nowcasting. NowcastDiT combines DyPro for temporally coherent forecasting with skill-aware post-training for meteorological alignment. Experiments on SEVIR and MRMS show strong performance in both meteorological skill and perceptual quality, supporting standard DiTs as a simple and scalable framework for precipitation nowcasting. Future work will evaluate its generalization across observation systems, resolutions, and longer forecast horizons. AI use statement AI tools assisted with drafting and revising portions of the manuscript, language polishing, literature search, figure preparation, verification of mathematical proof and use of the ICLR 2027 template. The authors personally reviewed and revised the AI-assisted content, verified its accuracy, and take full responsibility for the final manuscript, including all claims and results. References Aditi et al. (2026) N. Aditi, A. Ali, J. Allen, M. Antolini, A. Aubame, A. Azzolini, J. Bai, M. Bala, Y. Balaji, J. Bapst, et al. Cosmos 3: omnimodal world models for physical ai. arXiv. Cited by: §1, §1, §3. Ali et al. (2025) A. Ali, J. Bai, M. Bala, Y. Balaji, A. Blakeman, T. Cai, J. Cao, T. Cao, E. Cha, Y. Chao, et al. World simulation with video foundation models for physical ai. arXiv. Cited by: §3. Black et al. (2024) K. Black, M. Janner, Y. Du, I. Kostrikov, and S. Levine Training diffusion models with reinforcement learning. In ICLR, Cited by: §6. Blattmann et al. (2023a) A. Blattmann, T. Dockhorn, S. Kulal, D. Mendelevitch, M. Kilian, D. Lorenz, Y. Levi, Z. English, V. Voleti, A. Letts, et al. Stable video diffusion: scaling latent video diffusion models to large datasets. arXiv. Cited by: §4.1. Blattmann et al. (2023b) A. Blattmann, R. Rombach, H. Ling, T. Dockhorn, S. W. Kim, S. Fidler, and K. Kreis Align your latents: high-resolution video synthesis with latent diffusion models. In CVPR, Cited by: §4.1. Chang et al. (2024) P. Chang, J. Tang, M. Gross, and V. C. Azevedo How i warped your noise: a temporally-correlated noise prior for diffusion models. In ICLR, Cited by: §4.2, §6. Esser et al. (2024) P. Esser, S. Kulal, A. Blattmann, R. Entezari, J. Müller, H. Saini, Y. Levi, D. Lorenz, A. Sauer, F. Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. arXiv. Cited by: §6. Gao et al. (2022a) Z. Gao, C. Tan, L. Wu, and S. Z. Li Simvp: simpler yet better video prediction. In CVPR, Cited by: §5.1. Gao et al. (2023) Z. Gao, X. Shi, B. Han, H. Wang, X. Jin, D. Maddix, Y. Zhu, M. Li, and Y. B. Wang Prediff: precipitation nowcasting with latent diffusion models. In NeurIPS, Cited by: §D.1, §1, §5.1, §6. Gao et al. (2022b) Z. Gao, X. Shi, H. Wang, Y. Zhu, Y. B. Wang, M. Li, and D. Yeung Earthformer: exploring space-time transformers for earth system forecasting. In NeurIPS, Cited by: §D.1, §5.1. Ge et al. (2023) S. Ge, S. Nah, G. Liu, T. Poon, A. Tao, B. Catanzaro, D. Jacobs, J. Huang, M. Liu, and Y. Balaji Preserve your own correlation: a noise prior for video diffusion models. In ICCV, Cited by: §4.2, §6. Gong et al. (2024) J. Gong, L. Bai, P. Ye, W. Xu, N. Liu, J. Dai, X. Yang, and W. Ouyang CasCast: skillful high-resolution precipitation nowcasting via cascaded modelling. In ICML, Cited by: §1, §5.1, §6. Guen and Thome (2020) V. L. Guen and N. Thome Disentangling physical dynamics from unknown factors for unsupervised video prediction. In CVPR, Cited by: §5.1. Guo et al. (2025) X. Guo, Y. Zhang, B. Chen, H. Xu, J. Wang, and M. Long Dynamical diffusion: learning temporal dynamics with diffusion models. In ICLR, Cited by: §1, §4.2, §6. Gupta et al. (2024) A. Gupta, L. Yu, K. Sohn, X. Gu, M. Hahn, L. Fei-Fei, I. Essa, L. Jiang, and J. Lezama Photorealistic video generation with diffusion models. In ECCV, Cited by: §4.1, §6. Henry et al. (2020) A. Henry, P. R. Dachapally, S. S. Pawar, and Y. Chen Query-key normalization for transformers. In Findings of EMNLP, Cited by: §4.1, §6. Ho et al. (2020) J. Ho, A. Jain, and P. Abbeel Denoising diffusion probabilistic models. In NeurIPS, Cited by: §1. Ho and Salimans (2022) J. Ho and T. Salimans Classifier-free diffusion guidance. arXiv. Cited by: §A.2, §5.3. Jolliffe and Stephenson (2012) I. T. Jolliffe and D. B. Stephenson Forecast verification: a practitioner’s guide in atmospheric science. John Wiley & Sons. Cited by: §5.1. Li et al. (2025) J. Li, Y. Cui, T. Huang, Y. Ma, C. Fan, M. Yang, and Z. Zhong MixGRPO: unlocking flow-based grpo efficiency with mixed ode-sde. Cited by: §C.3, §4.3, §6. Lin et al. (2025) K. Lin, B. Zhang, D. Yu, W. Feng, S. Chen, F. Gao, X. Li, and Y. Ye AlphaPre: amplitude-phase disentanglement model for precipitation nowcasting. In CVPR, Cited by: §D.1, §5.1, §5.1. Lipman et al. (2023) Y. Lipman, R. T. Chen, H. Ben-Hamu, M. Nickel, and M. Le Flow matching for generative modeling. In ICLR, Cited by: §1. Liu et al. (2025) J. Liu, G. Liu, J. Liang, Y. Li, J. Liu, X. Wang, P. Wan, D. Zhang, and W. Ouyang Flow-grpo: training flow matching models via online rl. In NeurIPS, Cited by: §C.3, §4.3, §6. Ma et al. (2025) X. Ma, Y. Wang, X. Chen, G. Jia, Z. Liu, Y. Li, C. Chen, and Y. Qiao Latte: latent diffusion transformer for video generation. In TMLR, Cited by: §6. OpenAI (2024) OpenAI Sora: video generation models as world simulators. Note: https://openai.com/research/video-generation-models-as-world-simulatorsAccessed: 2024-04-01 Cited by: §3. Peebles and Xie (2023) W. Peebles and S. Xie Scalable diffusion models with transformers. In ICCV, Cited by: §1, §5.3, §6. Rombach et al. (2022) R. Rombach, A. Blattmann, D. Lorenz, P. Esser, and B. Ommer High-resolution image synthesis with latent diffusion models. In CVPR, Cited by: §D.1, §2. Schaefer (1990) J. T. Schaefer The critical success index as an indicator of warning skill. Weather and forecasting. Cited by: §5.1. Seedance et al. (2026) T. Seedance, D. Chen, L. Chen, X. Chen, Y. Chen, Z. Chen, Z. Chen, F. Cheng, T. Cheng, Y. Cheng, et al. Seedance 2.0: advancing video generation for world complexity. arXiv. Cited by: §1, §1, §3. Shao et al. (2024) Z. Shao, P. Wang, Q. Zhu, R. Xu, J. Song, X. Bi, H. Zhang, M. Zhang, Y. K. Li, Y. Wu, and D. Guo DeepSeekMath: pushing the limits of mathematical reasoning in open language models. arXiv. Cited by: §4.3. Shi et al. (2015) X. Shi, Z. Chen, H. Wang, D. Yeung, W. Wong, and W. Woo Convolutional lstm network: a machine learning approach for precipitation nowcasting. In NeurIPS, Cited by: §5.1. Song et al. (2021) Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole Score-based generative modeling through stochastic differential equations. In ICLR, Cited by: §1. Su et al. (2024) J. Su, M. Ahmed, Y. Lu, S. Pan, W. Bo, and Y. Liu Roformer: enhanced transformer with rotary position embedding. Neurocomputing. Cited by: §4.1, §6. Veillette et al. (2020) M. Veillette, S. Samsi, and C. Mattioli Sevir: a storm event imagery dataset for deep learning applications in radar and satellite meteorology. In NeurIPS, Cited by: §D.1, §D.2, §5.1. Voleti et al. (2022) V. Voleti, A. Jolicoeur-Martineau, and C. Pal Mcvd-masked conditional video diffusion for prediction, generation, and interpolation. In NeurIPS, Cited by: §4.1. Wan et al. (2025) T. Wan, A. Wang, B. Ai, B. Wen, C. Mao, C. Xie, D. Chen, F. Yu, H. Zhao, J. Yang, et al. Wan: open and advanced large-scale video generative models. arXiv preprint arXiv:2503.20314. Cited by: §1, §3, §4.1, §6. Wang et al. (2017) Y. Wang, E. D. Coning, A. Harou, and W. Jacobs Guidelines for nowcasting techniques. WMO-No. 1198 World Meteorological Organization, Geneva, Switzerland. Cited by: §1. Wang et al. (2004) Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing 13 (4), p. 600–612. Cited by: §D.2, §4.3, §5.1. Wen et al. (2026) P. Wen, M. He, P. Filippi, N. Zhao, F. Zhang, T. F. Bishop, Z. Wang, and K. Hu DuoCast: duo-probabilistic diffusion for precipitation nowcasting. In AAAI, Cited by: §1, §6. Wu et al. (2025) J. Wu, S. Yin, N. Feng, and M. Long RLVR-World: training world models with reinforcement learning. In Advances in Neural Information Processing Systems, Vol. 38. Cited by: §4.3, §6. Xue et al. (2025) Z. Xue, J. Wu, Y. Gao, F. Kong, L. Zhu, M. Chen, Z. Liu, W. Liu, Q. Guo, W. Huang, et al. Dancegrpo: unleashing grpo on visual generation. arXiv. Cited by: §1, §4.3, §6. Yang et al. (2024) Z. Yang, J. Teng, W. Zheng, M. Ding, S. Huang, J. Xu, Y. Yang, W. Hong, X. Zhang, G. Feng, et al. Cogvideox: text-to-video diffusion models with an expert transformer. arXiv. Cited by: §4.1, §6. Ye et al. (2026) S. Ye, Y. Ge, K. Zheng, S. Gao, S. Yu, G. Kurian, S. Indupuru, Y. L. Tan, C. Zhu, J. Xiang, et al. World action models are zero-shot policies. arXiv. Cited by: §3. Yu et al. (2024) D. Yu, X. Li, Y. Ye, B. Zhang, C. Luo, K. Dai, R. Wang, and X. Chen DiffCast: a unified framework via residual diffusion for precipitation nowcasting. In CVPR, Cited by: §D.1, §D.1, §D.2, §1, §5.1, §5.1, §6. Zhang et al. (2016) J. Zhang, K. Howard, C. Langston, B. Kaney, Y. Qi, L. Tang, H. Grams, Y. Wang, S. Cocks, S. Martinaitis, et al. Multi-radar multi-sensor (MRMS) quantitative precipitation estimation: initial operating capabilities. Bulletin of the American Meteorological Society 97 (4), p. 621–638. Cited by: §D.1, §5.1. Zhang et al. (2018) R. Zhang, P. Isola, A. A. Efros, E. Shechtman, and O. Wang The unreasonable effectiveness of deep features as a perceptual metric. In CVPR, Cited by: §D.2, §4.3, §5.1. Zhang et al. (2023) Y. Zhang, M. Long, K. Chen, L. Xing, R. Jin, M. I. Jordan, and J. Wang Skilful nowcasting of extreme precipitation with nowcastnet. Nature. Cited by: §D.1, §D.1, §D.2, §1, §5.1, §5.1. Zheng et al. (2026) K. Zheng, H. Chen, H. Ye, H. Wang, Q. Zhang, K. Jiang, H. Su, S. Ermon, J. Zhu, and M. Liu Diffusionnft: online diffusion reinforcement with forward process. In ICLR, Cited by: §5.3. Zhong et al. (2025) J. Zhong, X. Zhang, J. Wang, and M. Long Domain guidance: a simple transfer approach for a pre-trained diffusion model. In ICLR, Cited by: §C.5, §E.3. Appendix A Model Architecture and Configuration A.1 VAE Architecture and Training We adopt a 2D VAE which compress only the spatial resolution which acts independently across frames. The pretrained VAE provides the encoder E and decoder D and remains frozen during flow-matching pretraining and RL post-training. Table 2 summarizes its architecture and training settings. Table 2: VAE architecture and training configuration. Parameters include the encoder, decoder, and latent projections. Setting SEVIR MRMS Architecture Parameters 82M Input shape 25×1×128×12825× 1× 128× 128 24×1×256×25624× 1× 256× 256 Encoder stages 4 Residual blocks / encoder stage 2 Encoder channels [128, 256, 512, 512] Decoder stages 4 Residual blocks / decoder stage 3 Decoder channels [512, 512, 256, 128] Latent channels 16 Latent resolution 16×1616× 16 32×3232× 32 Spatial compression 8×8× Temporal compression 1×1× Normalization GroupNorm, 32 groups Activation SiLU Training # steps 1,488,000 2,000,000 Optimizer AdamW, (β1,β2)=(0.5,0.9)( _1, _2)=(0.5,0.9) Batch size 8 Learning rate 10−410^-4 Weight decay 0.01 EMA decay 0.9999 Gradient clipping norm 1.0 Adversarial warmup steps 100,000 A.2 Transformer Architecture, Training, and Inference Table 3 collects the default architecture, flow-matching pretraining settings, and pretrained-model inference configurations for MRMS and SEVIR. RL post-training settings are reported separately in Appendix C.6. Table 3: Transformer architecture, flow-matching pretraining, and inference configuration. Parameters include the conditioner, time embedding, and output layer. Inference settings refer to the pretrained-model evaluation configurations. Setting SEVIR MRMS Architecture Parameters 130M Frames (history / future) 5 / 20 4 / 20 Transformer blocks 12 Hidden dimension 768 Feedforward dimension 3072 Attention heads 12 Head dimension 64 Patch size 2×22× 2 Tokens per sample 25×8×8=160025× 8× 8=1600 24×16×16=614424× 16× 16=6144 Latent channels 16 Block normalization LayerNorm QK normalization RMSNorm Positional encoding 3D RoPE Time modulation adaLN-Zero FFN activation GELU History fusion Additive Training # steps 372,000 500,000 Optimizer AdamW, (β1,β2)=(0.9,0.95)( _1, _2)=(0.9,0.95) Batch size 32 Learning rate 10−410^-4 Learning rate schedule Constant EMA decay 0.9999 Gradient clipping norm 1.0 Time sampler Logit-normal, μ=−1μ=-1, σ=1σ=1 DyPro correlation strength α 0.5 Condition dropout 0.1 (zero conditioning) Inference Sampler Euler with DyPro (Algorithm 2) Sampling steps 10 Timestep grid Uniform in [0,1][0,1] CFG weight (without RL) 1.6 History Conditioning Let cond∈ℝB×T×C×H×Wz_cond ^B× T× C× H× W denote the conditioning sequence, which places the observed latent frames in the first L positions and masks the remaining future positions with zeros. The conditioner first applies a frame-wise convolutional patch encoder with the same patch size as the noisy-input embedder. It then adds a learnable spatial-topology embedding and a learnable frame-index embedding, followed by a SiLU activation and a zero-initialized 1×11× 1 convolution. Denoting the resulting condition features by c and the noisy patch embeddings by th_t, conditioning is performed through ~t=t+. h_t=h_t+c. (10) The conditioned embeddings are then flattened into spatiotemporal tokens and processed by the standard DiT blocks. Thus, the conditioner changes neither the Transformer blocks nor their input–output interface and requires no cross-attention or task-specific fusion pathway. Classifier-free guidance and Domain Guidance. During inference, we adopt classifier-free guidance that adjusts the influence of historical conditioning. Classifier-free guidance (Ho and Salimans, 2022) adjusts the influence of historical conditioning by combining conditional and unconditional velocity predictions from the same checkpoint. Let θpre _pre denote the parameters before RL post-training and let ∅ denote zero conditioning, consistent with the condition-dropout setting in Table 3. The guided prediction is CFG(t,t∣)=wθpre(t,t∣)+(1−w)θpre(t,t∣∅),v^CFG(z_t,t )=w\,v_ _pre(z_t,t )+(1-w)\,v_ _pre(z_t,t ), (11) where w is the guidance weight and w=1w=1 recovers the conditional prediction without guidance. We adopt w=1.6w=1.6 at pretraining stage. Appendix B Foundation, Training and Sampling with DyPro We describe the noise transform, training target, and deterministic sampling update associated with the DyPro parameterization in Section 4.2, followed by their distributional properties and continuous-time interpretation. The stochastic extension used for post-training is presented in Appendix B.4. Diffusion time increases from noise at t=0t=0 to data at t=1t=1. We condition throughout on the history c and write =1y=z_1 for the clean future latent sequence. Each of its S frames has d latent coordinates, so the flattened sequence has dimension m=Sdm=Sd. The Gaussian innovations are independent of y and c. Algorithm 3 DyPro Noise Correlation and Decorrelation ⬇ # xi, e: frame sequences; s indexes frames # t: diffusion timestep; alpha: shared DyPro strength def correlate(xi, t): a = alpha * (1 - t) q = 1 / sqrt(1 + a**2) r = a * q e = xi.copy() for s in range(1, len(xi)): e[s] = r * e[s - 1] + q * xi[s] return e def decorrelate(e, t): a = alpha * (1 - t) q = 1 / sqrt(1 + a**2) r = a * q xi = e.copy() for s in range(1, len(e)): xi[s] = (e[s] - r * e[s - 1]) / q return xi B.1 Correlated Noise For finite α≥0α≥ 0, define rt=γt=α(1−t)1+α2(1−t)2,qt=1−γt=11+α2(1−t)2.r_t= _t= α(1-t) 1+α^2(1-t)^2, q_t= 1- _t= 1 1+α^2(1-t)^2. (12) The frame-wise recursion defined in Equation 3, practically implemented through correlate in Algorithm 3, denotes a lower-triangular matrix representation. With frame indices s,j∈0,…,S−1s,j∈\0,…,S-1\, let (Ct)sj=rts,j=0,qtrts−j,1≤j≤s,0,j>s.t=Ct⊗d,ϵt=t,(C_t)_sj= casesr_t^s,&j=0,\\ q_tr_t^s-j,&1≤ j≤ s,\\ 0,&j>s. cases _t=C_t _d, ε_t=C_t ξ, (13) where ∼(,m) ξ (0,I_m) and rt0=1r_t^0=1, including when rt=0r_t=0. Because qt>0q_t>0, this transform is invertible. Its inverse t−1=C−1⊗dC_t^-1=C^-1 _d, implemented by decorrelate in Algorithm 3, follows directly from the recursion: 1=ϵt1,s=ϵts−rtϵts−1qt,s≥2. ξ^1= ε_t^1, ξ^s= ε_t^s-r_t ε_t^s-1q_t, s≥ 2. (14) The joint noise ϵt ε_t is Gaussian because it is a linear transform of independent Gaussian innovations. Since rt2+qt2=1r_t^2+q_t^2=1, the recursion preserves the standard Gaussian marginal of each frame. Independence of subsequent innovations gives Cov(ϵts,ϵtj)=rt|s−j|d=γt|s−j|/2dCov( ε_t^s, ε_t^j)=r_t^|s-j|I_d= _t^|s-j|/2I_d, yielding the full covariance and distribution t=tt⊤=[rt|s−j|]s,j=0S−1⊗d,ϵt∼(,t).Q_t=C_tC_t = [r_t^|s-j| ]_s,j=0^S-1 _d, ε_t (0,Q_t). (15) For α=0α=0, or at t=1t=1, rt=0r_t=0 and qt=1q_t=1, so t=mC_t=I_m and the noise is independent across frames. B.2 Linear Interpolation under Correlated Noise The linear interpolation between y and ϵt ε_t incorporates the time dependence of the noise transform. Holding y and ξ fixed, the interpolation path and its derivative are t _t =t+(1−t)ϵt=t+(1−t)t, =ty+(1-t) ε_t=ty+(1-t)C_t ξ, (16) ˙t z_t =−ϵt+(1−t)˙t. =y- ε_t+(1-t) C_t ξ. (17) Consequently, for t<1t<1, the conditional distribution along this path is pt(∣,)=(,t,(1−t)2t).p_t(z ,c)=N\! (z;ty,(1-t)^2Q_t ). (18) Marginalizing over ∼pdata(⋅∣)y p_data(· ) defines a probability path from p0=(,0)p_0=N(0,Q_0) to p1=pdata(⋅∣)p_1=p_data(· ). To express the path derivative in terms of the correlated noise, define t=˙tt−1,ϵ˙t=tϵt.B_t= C_tC_t^-1, ε_t=B_t ε_t. (19) The operator tB_t describes how the noise transform changes with diffusion time for fixed innovations. Averaging Equation 17 over the conditional distribution of the clean sequence and innovations gives the marginal velocity t(∣) _t(z ) =[˙t∣t=,] =E\! [ z_t _t=z,c ] =[−ϵt∣t=,]+(1−t)t[ϵt∣t=,]. =E\! [y- ε_t _t=z,c ]+(1-t)B_tE\! [ ε_t _t=z,c ]. (20) This velocity satisfies the continuity equation ∂tpt+∇⋅(ptt)=0 _tp_t+ _z·(p_tv_t)=0. The associated deterministic generative dynamics are therefore dtdt=t(t∣),0=0,∼(,m). dz_tdt=v_t(z_t ), _0=C_0 ξ, ξ (0,I_m). (21) B.3 Training Target and Deterministic Sampling Algorithm 1 regresses −ϵty- ε_t, providing a simple parameterization of the marginal velocity in Equation 20. Given one network prediction θ=θ(t,t∣)f_θ=f_θ(z_t,t ), the clean latent, correlated noise, and innovations are estimated as ^θ y_θ =t+(1−t)θ, =z_t+(1-t)f_θ, (22) ϵ^θ ε_θ =t−tθ, =z_t-tf_θ, ^θ ξ_θ =t−1ϵ^θ. =C_t^-1 ε_θ. These identities follow directly from the interpolation path: =t+(1−t)(−ϵt)y=z_t+(1-t)(y- ε_t) and ϵt=t−t(−ϵt) ε_t=z_t-t(y- ε_t). Substituting these estimates into Equation 20 gives the velocity estimate ^θ(t,t∣)=θ+(1−t)tϵ^θ=θ+(1−t)˙t^θ. v_θ(z_t,t )=f_θ+(1-t)B_t ε_θ=f_θ+(1-t) C_t ξ_θ. (23) For deterministic sampling, we integrate this velocity by holding the clean estimate ^θ y_θ fixed within each step from t to t′>t >t. Using Equation 22, the velocity can be written as ^θ(,t∣)=^θ−1−t+t(−t^θ). v_θ(z,t )= y_θ-z1-t+B_t (z-t y_θ ). (24) For τ∈[t,t′)τ∈[t,t ), define the residual τ=τ−τ^θw_τ=z_τ-τ y_θ. With the clean estimate fixed, its dynamics satisfy dτdτ=(τ−m1−τ)τ. dw_τdτ= (B_τ- I_m1-τ )w_τ. (25) Since dτ[(1−τ)τ]=(τ−m1−τ)(1−τ)τ, ddτ [(1-τ)C_τ ]= (B_τ- I_m1-τ )(1-τ)C_τ, (26) the residual has the closed-form update t′=1−t′1−tt′t−1t.w_t = 1-t 1-tC_t C_t^-1w_t. (27) Substituting t=(1−t)ϵ^θw_t=(1-t) ε_θ yields the deterministic sampling rule t′ _t =t′^θ+(1−t′)t′t−1ϵ^θ =t y_θ+(1-t )C_t C_t^-1 ε_θ =t′^θ+(1−t′)t′^θ. =t y_θ+(1-t )C_t ξ_θ. (28) The update is exact for the within-step dynamics with a fixed clean estimate and is first-order consistent with the learned ODE. It extends continuously to t′=1t =1, where it returns ^θ y_θ. Algorithm 2 implements this update by applying decorrelate at t and correlate at t′t . Each step uses one evaluation of θf_θ and transports the estimated innovations to the next timestep. For α=0α=0, t=mC_t=I_m throughout, and the update reduces to t′=t+(t′−t)θz_t =z_t+(t -t)f_θ. B.4 Stochastic Sampling Algorithm 4 DyPro SDE Sampling (w/o CFG) ⬇ # One active SDE transition: t -> t_next < 1 # kappa: stochasticity; 0 < kappa**2 * (t_next - t) <= 1 v = net(z, t, c) x = z + (1 - t) * v e = z - t * v e_init = decorrelate(e, t) a = kappa * sqrt(t_next - t) e_mean = sqrt(1 - a**2) * e_init e = correlate(e_mean + a * randn_like(e_init), t_next) z_next = t_next * x + (1 - t_next) * e mu = t_next * x + (1 - t_next) * correlate(e_mean, t_next) residual = decorrelate(stopgrad(z_next) - mu, t_next) scale = (1 - t_next) * a log_score = avg_latent_dims(normal_log_prob(residual, 0, scale)) return z_next, log_score A stochastic extension of the deterministic dynamics refreshes the noise in independent-innovation coordinates. Let κt≥0 _t≥ 0 be a prescribed stochasticity schedule independent of the policy parameters. We replace the fixed innovations with the Ornstein–Uhlenbeck process dt=−κt22tdt+κtdt,0∼(,m),d ξ_t=- _t^22 ξ_t\,dt+ _t\,dW_t, ξ_0 (0,I_m), (29) where tW_t is an m-dimensional standard Brownian motion, independent of the clean sequence and history. This process preserves the standard Gaussian distribution of the innovations at every timestep. Consequently, t=t+(1−t)ttz_t=ty+(1-t)C_t ξ_t retains the conditional distributions in Equation 18. Applying the product rule, taking conditional expectations given (t,)(z_t,c), and parameterizing them with the network predictions gives dt=[θ+(1−t)(t−κt22m)ϵ^θ]dt+κt(1−t)tdt.dz_t= [f_θ+(1-t) (B_t- _t^22I_m ) ε_θ ]dt+ _t(1-t)C_t\,dW_t. (30) Here, the network prediction and noise estimate are evaluated at (t,t,)(z_t,t,c). Setting κt=0 _t=0 recovers the deterministic dynamics. For a sampling step from t to t′>t >t with t′<1t <1, we hold the clean estimate ^θ y_θ fixed and discretize the innovation process in Equation 29 from ^θ ξ_θ using h=t′−th=t -t and a=κth,b=1−a2,0≤a≤1.a= _t h, b= 1-a^2, 0≤ a≤ 1. (31) Here, a2+b2=1a^2+b^2=1 preserves the standard Gaussian reference distribution in innovation coordinates. For an independent ∼(,m) η (0,I_m), the resulting update is t′=t′^θ+(1−t′)t′(bt−1ϵ^θ+a).z_t =t y_θ+(1-t )C_t (bC_t^-1 ε_θ+a η ). (32) All network estimates are evaluated at the current state (t,t,)(z_t,t,c). Algorithm 4 implements this update by decorrelating the predicted noise, mixing the resulting innovations with independent Gaussian noise, and applying the noise transform at t′t . For a=0a=0, the update reduces to Equation 28. Appendix C Timestep-aware post-training Post-training combines a terminal forecast reward with policy updates on selected stochastic transitions. We describe mixed rollouts, timestep-aware reward evaluation, and the local policy objective, together with the training algorithm and configuration. C.1 Mixed Sampling and Window Scheduling We discretize diffusion time as 0=t0<⋯<tN=10=t_0<·s<t_N=1 and activate a contiguous window ℓ=ℓ,…,ℓ+K−1W_ =\ ,…, +K-1\, with default size K=4K=4. The rollout policy θold _old is held fixed while collecting the group. Transitions inside the window use the stochastic kernel from Appendix B.4, while the remaining transitions use the deterministic update from Appendix B.3: tn+1=Sample[pDyProθold(⋅∣tn,)],n∈ℓ,ΦθoldDyPro(tn,tn,tn+1,),n∉ℓ.z_t_n+1= casesSample\! [p^DyPro_ _old(\,· _t_n,c) ],&n _ ,\\ ^DyPro_ _old(z_t_n,t_n,t_n+1,c),&n _ . cases (33) Here, pDyProp^DyPro is the transition distribution induced by Equation 32, and ΦDyPro ^DyPro denotes the deterministic update in Equation 28. The trajectories share an initial DyPro latent and conditioning context, with independent stochastic innovations inside the window. The stochastic window contains only nonterminal transitions, with 0<κtn2(tn+1−tn)≤10< _t_n^2(t_n+1-t_n)≤ 1 for each active step. Its bounds are 1≤K≤N−1,0≤ℓ≤ℓmax=N−K−1.1≤ K≤ N-1, 0≤ ≤ _ =N-K-1. (34) The final transition to tN=1t_N=1 is deterministic. We start at ℓ=0 =0 and cycle through window starts spaced by sws_w, switching after every MshiftM_shift training iterations: ℓ←ℓ+sw,ℓ+sw≤ℓmax,0,otherwise. ← cases +s_w,& +s_w≤ _ ,\\ 0,&otherwise. cases (35) With N=10N=10, K=4K=4, sw=2s_w=2, and Mshift=20M_shift=20 throughout post-training. C.2 Timestep-aware reward evaluation Each rollout produces a final decoded forecast ^i=D(1i) x^i=D(z_1^i), which is compared with the reference future sequence ∗x^*. The two reward components are defined in Equations 7 and 8: RnoiseR_noise combines pooled low-threshold CSI with SSIM, and RcleanR_clean combines high-threshold CSI with negative LPIPS. Local max pooling applies only to the low-threshold CSI terms; the other metrics are evaluated on the decoded forecast without this pooling operation. Metric definitions are given in Appendix D.2. For an active transition n, the terminal reward assigned to trajectory i is Rni=R(^i,∗,tn)R_n^i=R( x^i,x^*;t_n), as defined in Equation 9. All active transitions are evaluated on the same final forecast. Their metric weights depend on their own diffusion times tnt_n, so rewards and group-relative advantages are computed separately for each transition. No reward is evaluated on an intermediate noisy latent. C.3 MixGRPO Objective and Policy Scores For each active transition n, the group provides a relative measure of forecast quality. We normalize its terminal rewards across the G trajectories: A^ni=Rni−mean(Rnjj=1G)std(Rnjj=1G)+εA, A^i_n= R_n^i-mean(\R_n^j\_j=1^G)std(\R_n^j\_j=1^G)+ _A, (36) where εA>0 _A>0 stabilizes the denominator. The comparison is made across forecasts at the same transition, rather than across diffusion times. If all group rewards agree, their advantages are zero. For a stochastic step from t to t′<1t <1 with a>0a>0, the update in Equation 32 defines the conditional density pθDyPro(′∣,) p^DyPro_θ(z ,c) =(′,θ,σ2t′), =N (z ; μ_θ,σ^2Q_t ), (37) θ μ_θ =t′^θ+(1−t′)bt′t−1ϵ^θ,σ=(1−t′)a. =t y_θ+(1-t )bC_t C_t^-1 ε_θ, σ=(1-t )a. (38) All network estimates are evaluated at (,t,)(z,t,c); the transition times are implicit in pθDyProp^DyPro_θ. Whitening the residual as θ=t′−1(′−θ)w_θ=C_t ^-1(z - μ_θ) gives the joint log density logpθDyPro(′∣,)=−m2log(2π)−mlogσ−log|dett′|−‖θ‖222σ2. p^DyPro_θ(z ,c)=- m2 (2π)-m σ- | _t |- \|w_θ\|_2^22σ^2. (39) For trajectory i at transition n, we write logpθ,ni=logpθDyPro(tn+1i∣tni,) p_θ,n^i= p^DyPro_θ(z_t_n+1^i _t_n^i,c), with logpold,ni p_old,n^i defined analogously for θold _old. For a stored state and successor from the rollout, the policy ratio is ρni(θ)=pθDyPro(tn+1i∣tni,)pθoldDyPro(tn+1i∣tni,)=exp(logpθ,ni−logpold,ni),ρ^i_n(θ)= p^DyPro_θ(z^i_t_n+1 ^i_t_n,c)p^DyPro_ _old(z^i_t_n+1 ^i_t_n,c)= ( p^i_θ,n- p^i_old,n ), (40) Both policies are evaluated on the same stored transition. The states, terminal rewards, advantages, and old-policy scores are held fixed during the update; gradients flow through the current-policy log density. When both policies share the time grid, α, and stochasticity schedule, their covariance and whitening Jacobian are identical and independent of θ. Let θ,niw^i_θ,n and σn _n denote the residual and scale in Equation 39 for trajectory i at transition n. Cancelling the shared terms in the two log densities yields logρni(θ)=‖old,ni‖22−‖θ,ni‖222σn2. ρ^i_n(θ)= \|w^i_old,n\|_2^2-\|w^i_θ,n\|_2^22 _n^2. (41) The Jacobian can thus be omitted from a score used only in this difference, although it remains part of the absolute joint log density. Following MixGRPO (Li et al., 2025) and Flow-GRPO (Liu et al., 2025), we maximize the clipped local surrogate MixGRPO(θ)=[1G|ℓ|∑i=1G∑n∈ℓmin(ρni(θ)A^ni,clip(ρni(θ),1−εc,1+εc)A^ni)],J_MixGRPO(θ)=E [ 1G|W_ | _i=1^G _n _ (ρ^i_n(θ) A^i_n,clip(ρ^i_n(θ),1- _c,1+ _c) A^i_n ) ], (42) where the expectation is over conditioning examples and old-policy rollouts, |ℓ|=K|W_ |=K, and εc _c is the clipping range. The implemented minimization loss is the negative of this objective. Only the stochastic transitions participate in the surrogate; deterministic transitions still influence the sampled final forecast. C.4 Training Algorithm Algorithm 5 presents the full training loop. The helper clipped_mixgrpo optimizes the negative of Equation 42, holding the rollout data fixed. Old-policy scores are cached internally, following the convention in Appendix C.3. The stochastic helper dypro_sde_step implements Equation 32 and obtains the next time from the grid. The deterministic helper ode_step denotes ΦDyPro ^DyPro, and max_left is the bound in Equation 34. The helper shared_noise(G) repeats one DyPro initial latent across the group. Both reward helpers include the specified metric coefficients, and group_normalize includes εA _A. Contexts and targets are broadcast as needed. Latent denormalization is included in decode. Algorithm 5 Stage-Aware Post-Training with Window Scheduling ⬇ # theta: trainable policy initialized from the flow-matching checkpoint # K: active-window size (default: 4); max_left: last valid window start left = 0 for iteration, (c, x_gt) in enumerate(dataloader): window = range(left, left + K) traj[:, 0] = shared_noise(G) for n, t in enumerate(timesteps[:-1]): if n in window: traj[:, n + 1] = dypro_sde_step(theta, traj[:, n], t, c) else: traj[:, n + 1] = ode_step(theta, traj[:, n], t, c) x_sample = decode(traj[:, -1]) r_noise = R_noise(x_sample, x_gt) r_clean = R_clean(x_sample, x_gt) for n in window: t = timesteps[n] rewards[:, n] = (1 - t) * r_noise + t * r_clean advantages = group_normalize(rewards[:, window], dim=0) loss = clipped_mixgrpo(theta, traj, window, advantages) update(theta, loss) if (iteration + 1) % shift_interval == 0: left += window_stride if left > max_left: left = 0 C.5 Domain Guidance After skill-aware RL post-training, we adopt Domain Guidance (DoG) (Zhong et al., 2025), which combines an adapted conditional model with the original pretrained model as the unconditional reference. In our setting, the conditional branch uses the RL-adapted parameters θRL _RL with history c, while the unconditional branch uses the frozen pre-RL parameters θpre _pre with zero conditioning: DoG(t,t∣)=wθRL(t,t∣)+(1−w)θpre(t,t∣∅).v^DoG(z_t,t )=w\,v_ _RL(z_t,t )+(1-w)\,v_ _pre(z_t,t ). (43) This retains the pretrained unconditional reference while incorporating skill alignment through the conditional branch. Setting w=1w=1 recovers the RL model without guidance; using θpre _pre for both branches recovers Equation 11. Post-RL evaluation settings use w=1.4w=1.4, as listed in Tables 4. Guidance is disabled during RL rollouts and applied only at inference. RL+CFG configuration in Appendix E.3 uses this DoG formulation. C.6 Post-Training and Reward Configuration Table 4 summarizes the post-training, reward, and evaluation configurations. The pretrained VAE remains frozen throughout post-training. Each rollout batch is used for one gradient update, followed by synchronization of the rollout policy. The CSI coefficients incorporate uniform averaging within each threshold subset and the mixing weights for SSIM or negative LPIPS. No additional normalization is applied to the weighted sums in Equations 7 and 8. The listed checkpoints identify the models used for evaluation, rather than the total training budgets. Table 4: Post-training, reward, and evaluation configurations. Reward thresholds are expressed in VIL values for SEVIR and mh−1m\,h^-1 for MRMS. Setting SEVIR MRMS Optimization Optimizer AdamW, (β1,β2)=(0.9,0.95)( _1, _2)=(0.9,0.95) Learning rate 10−510^-5, constant Batch size 8 Policy ratio clipping range εc _c 10−410^-4 Advantage clipping [−5,5][-5,5] Rollout Group size G 16 Sampling steps N 10 Stochastic window size K 4 Window stride sws_w 2 Window shift interval MshiftM_shift 20 training iterations (cyclic) DyPro correlation strength α 0.5 CFG during rollout Disabled Reward Low-threshold set lowT_low 16,74,133\16,74,133\ 1,2,4\1,2,4\ High-threshold set highT_high 160,181,219\160,181,219\ 8,16,32\8,16,32\ Low-threshold CSI max pooling 4×44× 4 SSIM coefficient λs _s 0.5 LPIPS coefficient λp _p 0.9 CSI coefficient λτ _τ, τ∈lowτ _low (1−λs)/|low|(1- _s)/|T_low| CSI coefficient λτ _τ, τ∈highτ _high (1−λp)/|high|(1- _p)/|T_high| Evaluation # steps 1,000 4,000 Sampling 10 Euler steps CFG weight 1.4 Appendix D Datasets and Evaluation Protocol D.1 Datasets and Preprocessing Table 5 summarizes the dataset configurations and split sizes for the forecasting tasks in Section 5.1. Table 5: Dataset configurations. Spatial resolution refers to the source radar grids, and frame size denotes the model input and output size. Forecast frames are shown as observed → predicted; split sizes count sequences. Setting SEVIR MRMS Data variable VIL Precipitation rate Spatial / temporal res. 1km1~km / 5min5~min 0.01∘0.01 / 10min10~min Forecast frames 5→205→ 20 4→204→ 20 Frame size 128×128128× 128 256×256256× 256 Train / validation / test 59,530 / 28,145 / 7,220 6,807,528 / 12,000 / 12,000 SEVIR (Veillette et al., 2020) contains spatiotemporal observations of weather events across the United States, each covering 384km×384km384~km× 384~km. Following prior studies (Gao et al., 2022b; Gao et al., 2023), we use the VIL modality, which has a native spatial resolution of 1 km and a temporal resolution of 5 minutes. Following DiffCast and AlphaPre (Yu et al., 2024; Lin et al., 2025), we downsample the frames to 128×128128× 128 and predict 20 future frames from 5 observed frames. Training includes events up to January 1, 2019. Validation uses later events up to October 1, 2019, and testing uses events after that date. Both cutoffs are inclusive for the earlier split and refer to 00:00 UTC. We exclude events with missing VIL data or duplicate VIL records. From each 49-frame event, we extract 25-frame sequences every five frames. Training augmentation uses rotations by multiples of 90∘90 and horizontal or vertical flips, applied consistently across all frames in a sequence. Since SEVIR stores VIL as dimensionless encoded values, we report its color bars and evaluation thresholds without physical units (Veillette et al., 2020). MRMS (Zhang et al., 2016) is a composite radar dataset collected over the contiguous United States, spanning 20∘20 N–55∘55 N in latitude and 130∘130 W–60∘60 W in longitude at a spatial resolution of 0.01∘0.01 per grid. Following NowcastNet (Zhang et al., 2023), we use data from 2016–2020 for model development and 2021 for testing. Within 2016–2020, we reserve the first day of each month for validation and use the remaining days for training. After excluding known anomalous timestamps, we take the last 24 frames of each continuous 40-frame sequence sampled at 10-minute intervals. For training, we sample sequences with replacement and select 256×256256× 256 crops from 512×512512× 512 patches, using precomputed sequence and spatial weights. Validation and testing use fixed sequence selections and 256×256256× 256 center crops. Radar and latent normalization. For SEVIR, we normalize VIL values by dividing by 255, following DiffCast (Yu et al., 2024). For MRMS, we cap rain rates at 128mh−1128~m\,h^-1 following NowcastNet (Zhang et al., 2023), then apply logarithmic normalization to [−1,1][-1,1]. For both datasets, we standardize VAE latents using dataset-specific means and standard deviations, building on latent rescaling in latent diffusion models (Rombach et al., 2022). D.2 Evaluation Metrics and Aggregation For meteorological skill, we use the Critical Success Index (CSI) and Heidke Skill Score (HSS) (Veillette et al., 2020; Yu et al., 2024; Zhang et al., 2023): CSIτ=TPτTPτ+FPτ+FNτ,CSI_τ= TP_τTP_τ+FP_τ+FN_τ, (44) and HSSτ=2(TPτ⋅TNτ−FPτ⋅FNτ)(TPτ+FNτ)(FNτ+TNτ)+(TPτ+FPτ)(FPτ+TNτ).HSS_τ= 2(TP_τ·TN_τ-FP_τ·FN_τ)(TP_τ+FN_τ)(FN_τ+TN_τ)+(TP_τ+FP_τ)(FP_τ+TN_τ). (45) Here, TPτTP_τ, FPτFP_τ, FNτFN_τ, and TNτTN_τ denote pixelwise true-positive, false-positive, false-negative, and true-negative counts at threshold τ, aggregated over the evaluation set at each lead time. We average CSI and HSS uniformly over lead times and evaluation thresholds. For perceptual quality, we use LPIPS (Zhang et al., 2018) and SSIM (Wang et al., 2004): LPIPS(^,∗)=∑ℓ1HℓWℓ∑h,w,caℓc(ϕℓ(^)hwc−ϕℓ(∗)hwc)2,LPIPS( x,x^*)= _ 1H_ W_ _h,w,ca_ c ( _ ( x)_hwc- _ (x^*)_hwc )^2, (46) where ϕℓ _ denotes channel-normalized features at layer ℓ , aℓca_ c are learned channel weights, and Hℓ,WℓH_ ,W_ are the feature-map dimensions. SSIM is defined as SSIM(^,∗)=(2μx^μx∗+c1)(2σx^x∗+c2)(μx^2+μx∗2+c1)(σx^2+σx∗2+c2),SSIM( x,x^*)= (2 _ x _x^*+c_1)(2 _ xx^*+c_2)( _ x^2+ _x^*^2+c_1)( _ x^2+ _x^*^2+c_2), (47) where μ, σ2σ^2, and σx^x∗ _ xx^* denote local means, variances, and covariance, and c1,c2c_1,c_2 are stabilization constants. Perceptual scores are spatially averaged within each frame and then uniformly averaged over forecast frames and test sequences. Higher CSI, HSS, and SSIM and lower LPIPS indicate better performance. Appendix E Additional Experimental Results E.1 Forecast Skill Across Lead Times Figure 6 compares CSI and HSS across forecast lead times on MRMS and SEVIR, complementing the aggregate results in Table 1. The curves cover 10–200 minutes on MRMS and 5–100 minutes on SEVIR and include NowcastDiT both with and without RL post-training. E.2 Cumulative Component Ablation Table 6 reports a cumulative ablation on SEVIR, starting from the standard DiT baseline and successively adding 3D RoPE and QK-Norm, DyPro, and timestep-aware RL. Each row retains all components introduced in the preceding rows. Table 6: Cumulative component ablation on SEVIR. ↑ indicates higher is better and ↓ indicates lower is better. Bold and underlined values denote the best and second-best results, respectively. Method CSI↑ CSI-181↑ CSI-219↑ HSS↑ LPIPS↓ SSIM↑ DiT 0.2926 0.0948 0.0555 0.3733 0.1545 0.7048 + 3D RoPE, QK-Norm 0.3012 0.1082 0.0676 0.3647 0.1317 0.6812 + DyPro 0.3195 0.1204 0.0752 0.4092 0.1486 0.7099 + RL 0.3240 0.1241 0.0750 0.4148 0.1469 0.7197 E.3 CFG and Skill-Aware Post-Training We adopt Domain Guidance (DoG) (Zhong et al., 2025) to integrate CFG with RL post-training, as detailed in Appendix C.5. Table 7 reports the individual and combined effects of CFG and RL. The combined configuration has the highest aggregate CSI, HSS, and SSIM among these four settings, while CFG alone has the lowest LPIPS, illustrating that the metrics need not improve together. Table 7: Effects of RL and classifier-free guidance on SEVIR. ↑ indicates higher is better and ↓ indicates lower is better. Bold and underlined values denote the best and second-best results, respectively. RL Guidance CSI↑ CSI-181↑ CSI-219↑ HSS↑ LPIPS↓ SSIM↑ ✘ ✘ 0.2934 0.0956 0.0560 0.3749 0.1541 0.7041 ✘ ✔ 0.3195 0.1204 0.0752 0.4092 0.1486 0.7099 ✔ ✘ 0.3109 0.1050 0.0588 0.3961 0.1580 0.7156 ✔ ✔ 0.3240 0.1241 0.0750 0.4148 0.1469 0.7197 E.4 DyPro Correlation Strength Table 8 reports the SEVIR sensitivity to α across meteorological and perceptual metrics. Among the listed settings, α=0.5α=0.5 gives the highest aggregate CSI. This experiment varies the noise correlation strength. All experiments in this ablation are conducted without RL post-training to isolate the effect of DyPro. Table 8: DyPro correlation strength α on SEVIR. α=0α=0 corresponds to the standard i.i.d. Gaussian noise prior. ↑ indicates higher is better and ↓ indicates lower is better. Bold and underlined values denote the best and second-best results, respectively. α CSI↑ CSI-181↑ CSI-219↑ HSS↑ LPIPS↓ SSIM↑ 0.00 0.3012 0.1082 0.0676 0.3647 0.1317 0.6812 0.25 0.3188 0.1184 0.0759 0.4075 0.1485 0.7090 0.33 0.3191 0.1192 0.0742 0.4080 0.1483 0.7097 0.50 0.3195 0.1204 0.0752 0.4092 0.1486 0.7099 0.66 0.3185 0.1194 0.0740 0.4077 0.1495 0.7098 0.75 0.3184 0.1184 0.0750 0.4084 0.1494 0.7092 E.5 Timestep-aware reward variants Table 9 defines the six variants in Figures 5(d) and 7. Let CLC_L and CHC_H denote mean low-threshold pooled CSI and mean high-threshold CSI, using the threshold sets and pooling in Table 4, and let S=SSIMS=SSIM and P=LPIPSP=LPIPS. The mixed components are Ms=0.5CL+0.5SM_s=0.5C_L+0.5S and Md=0.1CH−0.9PM_d=0.1C_H-0.9P. Table 9: Terminal rewards for the six ablation settings. Reward Static Timestep-aware Mixed (Ms+Md)/2(M_s+M_d)/2 (1−t)Ms+tMd(1-t)M_s+tM_d CSI (CL+CH)/2(C_L+C_H)/2 (1−t)CL+tCH(1-t)C_L+tC_H Perceptual (0.1S−0.9P)/2(0.1S-0.9P)/2 0.1(1−t)S−0.9tP0.1(1-t)S-0.9tP For the timestep-aware perceptual reward, Rnoise=0.1SR_noise=0.1S and Rclean=−0.9PR_clean=-0.9P, so the reward shifts from SSIM at the noise endpoint to negative LPIPS at the clean endpoint. The static counterpart averages these two endpoint rewards, following the same convention as the CSI and mixed variants. This reward changes the relative weighting of structural agreement and perceptual similarity across denoising transitions. All six variants share the cyclic window schedule in Appendix C.1; the contribution of window scheduling is not separately ablated. E.6 Additional Visualizations We provide four additional forecast visualizations to complement the qualitative comparisons in the main text. Figures 8 and 9 show SEVIR cases 802 and 6155, comparing NowcastDiT with CasCast and the standard DiT baseline. Figures 10 and 11 show MRMS cases 239 and 1149, comparing NowcastDiT with NowcastNet and the standard DiT baseline. Each figure includes the input observations, ground truth, and forecasts at matched lead times, allowing comparison of precipitation structure and intensity evolution. These selected cases supplement the aggregate evaluation in Table 1. Figure 6: Forecast skill across lead times on MRMS and SEVIR. The horizontal axes show forecast lead time in minutes; higher CSI and HSS indicate better performance. Figure 7: Additional reward ablations on SEVIR. LPIPS (left) and RMSE (right) during RL training for the rewards in Table 9. The legend follows Figure 5(d); the timestep-aware perceptual reward uses 0.1(1−t)SSIM−0.9tLPIPS0.1(1-t)SSIM-0.9tLPIPS. Lower values indicate better performance for both metrics. Figure 8: Qualitative comparison on SEVIR (case 802). Five input observations span −20-20 to 00 minutes at 5-minute intervals. Ground truth and forecasts are shown every 10 minutes up to 100 minutes. Colors indicate VIL values. Figure 9: Qualitative comparison on SEVIR (case 6155). Five input observations span −20-20 to 00 minutes at 5-minute intervals. Ground truth and forecasts are shown every 10 minutes up to 100 minutes. Colors indicate VIL values. Figure 10: Qualitative comparison on MRMS (case 239). Four input observations span −30-30 to 00 minutes at 10-minute intervals. Ground truth and forecasts are shown every 20 minutes up to 200 minutes. Colors indicate precipitation rate in m h-1. Figure 11: Qualitative comparison on MRMS (case 1149). Four input observations span −30-30 to 00 minutes at 10-minute intervals. Ground truth and forecasts are shown every 20 minutes up to 200 minutes. Colors indicate precipitation rate in m h-1.