In ill-posed imaging inverse problems, there can exist many hypotheses that fit both the observed measurements and prior knowledge of the true image. Rather than returning just one hypothesis of that image, posterior samplers aim to explore the full solution space by generating many probable hypotheses, which can later be used to quantify uncertainty or construct recoveries that appropriately navigate the perception/distortion trade-off. In this work, we propose a fast and accurate posterior-sampling conditional generative adversarial network (cGAN) that, through a novel form of regularization, aims for correctness in the posterior mean as well as the trace and K principal components of the posterior covariance matrix. Numerical experiments demonstrate that our method outperforms competitors in a wide range of ill-posed imaging inverse problems.

Conditional generative adversarial networks (cGANs) have gained a considerable attention in recent years due to its class-wise controllability and superior quality for complex generation tasks. We introduce a simple yet effective approach to improving cGANs by measuring the discrepancy between the data distribution and the model distribution on given samples. The proposed measure, coined the gap of log-densities (GOLD), provides an effective self-diagnosis for cGANs while being efficiently, computed from the discriminator. We propose three applications of the GOLD: example re-weighting, rejection sampling, and active learning, which improve the training, inference, and data selection of cGANs, respectively. Our experimental results demonstrate that the proposed methods outperform corresponding baselines for all three applications on different image datasets.

Conditional Generative Adversarial Networks (cGANs) are implicit generative models which allow to sample from class-conditional distributions. Existing cGANs are based on a wide range of different discriminator designs and training objectives. One popular design in earlier works is to include a classifier during training with the assumption that good classifiers can help eliminate samples generated with wrong classes. Nevertheless, including classifiers in cGANs often comes with a side effect of only generating easy-to-classify samples. Recently, some representative cGANs avoid the shortcoming and reach state-of-the-art performance without having classifiers.

Accurately predicting short-term precipitation is critical for weather-sensitive applications such as disaster management, aviation, and urban planning. Traditional numerical weather prediction can be computationally intensive at high resolution and short lead times. In this work, we propose a lightweight UNet-based encoder-decoder augmented with axial-attention blocks that attend along image rows and columns to capture long-range spatial interactions, while temporal context is provided by conditioning on multiple past radar frames. Our hybrid architecture captures both local and long-range spatio-temporal dependencies from radar image sequences, enabling fixed lead-time precipitation nowcasting with modest compute. Experimental results on a preprocessed subset of the HKO-7 radar dataset demonstrate that our model outperforms ConvLSTM, pix2pix-style cGANs, and a plain UNet in pixel-fidelity metrics, reaching PSNR 47.67 and SSIM 0.9943. We report PSNR/SSIM here; extending evaluation to meteorology-oriented skill measures (e.g., CSI/FSS) is left to future work. The approach is simple, scalable, and effective for resource-constrained, real-time forecasting scenarios.

Climate change has intensified the frequency and severity of wildfires, making rapid and accurate prediction of fire spread essential for effective mitigation and response. Physics-based simulators such as FARSITE offer high-fidelity predictions but are computationally intensive, limiting their applicability in real-time decision-making, while existing deep learning models often yield overly smooth predictions that fail to capture the complex, nonlinear dynamics of wildfire propagation. This study proposes an autoregressive conditional generative adversarial network (CGAN) for probabilistic wildfire spread prediction. By formulating the prediction task as an autoregressive problem, the model learns sequential state transitions, ensuring long-term prediction stability. Experimental results demonstrate that the proposed CGAN-based model outperforms conventional deep learning models in both overall predictive accuracy and boundary delineation of fire perimeters. These results demonstrate that adversarial learning allows the model to capture the strong nonlinearity and uncertainty of wildfire spread, instead of simply fitting the pixel average. Furthermore, the autoregressive framework facilitates systematic temporal forecasting of wildfire evolution. The proposed CGAN-based autoregressive framework enhances both the accuracy and physical interpretability of wildfire spread prediction, offering a promising foundation for time-sensitive response and evacuation planning.

We present a new type of probabilistic model which we call DISsimilarity COefficient Networks (DISCO Nets).

We would like to thank all reviewers evaluating the paper, and will fully address all the review concerns in the revision. We have recently tested VGG face using 2000 classes. The FID score of T AC-GAN and PcGAN are 13.79 and 22.42. This indicates that the drawbacks in AC-GAN loss cannot be fully addressed by pacGAN. We would like to thank R#2 for very detailed comments.

Our experimental results demonstrate that the proposed methods outperform corresponding baselines for all three applications on different image datasets.

We would like to thank all reviewers evaluating the paper, and will fully address all the review concerns in the revision. We have recently tested VGG face using 2000 classes. The FID score of T AC-GAN and PcGAN are 13.79 and 22.42. This indicates that the drawbacks in AC-GAN loss cannot be fully addressed by pacGAN. We would like to thank R#2 for very detailed comments.