Diffusion models have demonstrated remarkable success in image generation, yet a persistent challenge remains: the bias between model predictions and the target distribution. In this paper, we propose a Bidirectional Noise Injection framework for enhancing diffusion models, implemented via Coordinated Input-Output Perturbation (CIOP). Our approach mitigates this bias by randomly applying synchronized noise injection to both the model inputs and the prediction targets during the training stage. This stochastic, synchronized noise injected acts as a smoothing mechanism that effectively reduces the 2-Wasserstein distance between the predicted and target distributions, as substantiated by our theoretical analysis based on optimal transport theory. Extensive experiments on multiple benchmark datasets and various generative tasks demonstrate that our method improves generation quality and training efficiency without incurring additional computational cost. Furthermore, the design of CIOP enables seamless integration with existing diffusion model improvements and advanced frameworks, thereby broadening its applicability. These results highlight the potential of Bidirectional Noise Injection via CIOP to alleviate bias in diffusion-based generative models across a wide range of settings.

We propose a channel modeling using jumpdiffusion processes, and study the differential properties of entropy and mutual information. By utilizing the Kramers-Moyal and Kolmogorov equations, we express the mutual information between the input and the output in series and integral forms, presented by Fisher-type information and mismatched KL divergence. We extend de Bruijn's identity and the I-MMSE relation to encompass general Markov processes.

We study the convexity of mutual information as a function of time along the Fokker-Planck flow. The results are generalizations of that along heat flow and Ornstein-Ulenbeck flow, which were established by A. Wibisono and V. Jog. We prove the existence and uniqueness of the classical solutions to a class of Fokker-Planck equations and then we obtain the second derivative of mutual information along the Fokker-Planck equation. If the initial distribution is sufficiently strongly logconcave compared to the steady state, then mutual information always preserves convexity under suitable conditions. In particular, if there exists some time point at which the distribution is sufficiently strongly log-concave, then mutual information will preserve convexity after that time.

Marine vibrators (MVibs) are increasingly used in seismic surveys due to their precise waveform control, flexible signal design, environmental friendliness, and enhanced low-frequency output. However, their long-duration pilot sweeps introduce challenges not present with traditional airguns—most notably, the Doppler effect. The simulation or correction of phase distortion can be achieved using frequency-wavenumber (F-K) domain dephasing operator equation based on the instantaneous frequency function, while they require sufficient spatial sampling to get the reliable effect. Besides, as a typical coherent noise source, the removal of surface-related multiple greatly determines seismic imaging quality. Although surface-related multiple elimination (SRME) scheme can suppress the interference, moderate phase, timing, amplitude errors, and clutter in predicted signal components are detrimental. We propose an Bayesian primary-multiple separation and Doppler-shift correction iterative framework that assumes the predictions from SRME-type techniques are approximately independent in the shearlet domain and robustly corrects and separates them. In our approach, the energy mismatch between separated and predicted components is effectively controlled. Synthetic and field data examples have shown that its key advancements include: (1) The F-K domain phase distortion operator based on the instantaneous frequency function cleverly matches with the shearlet dictionary to simulate source motion in the sparsity-promoting inversion, reducing computational costs by 35.02 %. (2) The introduction of linear moveout (LMO) overcomes the sensitivity of Doppler-shift correction to spatial aliasing and achieves a 18.0742 dB signal-to-noise ratio (SNR) improvement in phase correction. (3) An improved threshold function is proposed to optimize primary-multiple separation, aiming at the shortcomings of the traditional ones. It outperforms the hard and soft threshold functions regarding average SNR, with improvements of 0.97 % and 6.21 %, respectively. Our approach only requires about 10 iterations to attain the converged solution.

This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i) The high-order derivatives of the network output with respect to the input variables are all zero. (ii) The DNN can be used on occluded samples, and when the input sample is less occluded, the DNN will yield higher confidence. (iii) The confidence of the DNN does not significantly degrade on occluded samples. These conditions are quite common, and we prove that under these conditions, the DNN will only encode a relatively small number of sparse interactions between input variables. Moreover, we can consider such interactions as symbolic primitive inference patterns encoded by a DNN, because we show that inference scores of the DNN on an exponentially large number of randomly masked samples can always be well mimicked by numerical effects of just a few interactions.

Wyner-Ziv video coding is a new paradigm for video compression, in which the prediction frames are possibly only available at the decoder. It exploits the redundancy between the source frame and the prediction frame at the decoder by utilizing their correlation information. However, such correlation information is difficult to estimate due to the absence of the prediction frame at the encoder and the lack of the source frame at the decoder. In this paper, we focus on this issue and propose a progressive adaptive correlation estimation (PACE) approach, in which the correlation information is progressively learned during the decoding process. Compared with our previous TRACE approach, PACE has similar performance in estimation accuracy as well as rate-distortion. Furthermore, it can be potentially integrated into more extensive WZVC applications, such as scalable applications and error-resilience applications.