Generating lifelike conversational avatars requires modeling not just isolated speakers, but the dynamic, reciprocal interaction of speaking and listening. However, modeling the listener is exceptionally challenging: direct audio-driven training fails, producing stiff, static listening motions. This failure stems from a fundamental imbalance: the speaker's motion is strongly driven by speech audio, while the listener's motion primarily follows an internal motion prior and is only loosely guided by external speech. This challenge has led most methods to focus on speak-only generation. The only prior attempt at joint generation relies on extra speaker's motion to produce the listener. This design is not end-to-end, thereby hindering the real-time applicability. To address this limitation, we present UniLS, the first end-to-end framework for generating unified speak-listen expressions, driven by only dual-track audio. Our method introduces a novel two-stage training paradigm. Stage 1 first learns the internal motion prior by training an audio-free autoregressive generator, capturing the spontaneous dynamics of natural facial motion. Stage 2 then introduces the dual-track audio, fine-tuning the generator to modulate the learned motion prior based on external speech cues. Extensive evaluations show UniLS achieves state-of-the-art speaking accuracy. More importantly, it delivers up to 44.1\% improvement in listening metrics, generating significantly more diverse and natural listening expressions. This effectively mitigates the stiffness problem and provides a practical, high-fidelity audio-driven solution for interactive digital humans.

Reliable reinforcement learning (RL) for diffusion large language models (dLLMs) requires both accurate advantage estimation and precise estimation of prediction probabilities. Existing RL methods for dLLMs fall short in both aspects: they rely on coarse or unverifiable reward signals, and they estimate prediction probabilities without accounting for the bias relative to the true, unbiased expected prediction probability that properly integrates over all possible decoding orders. To mitigate these issues, we propose \emph{d}-TreeRPO, a reliable RL framework for dLLMs that leverages tree-structured rollouts and bottom-up advantage computation based on verifiable outcome rewards to provide fine-grained and verifiable step-wise reward signals. When estimating the conditional transition probability from a parent node to a child node, we theoretically analyze the estimation error between the unbiased expected prediction probability and the estimate obtained via a single forward pass, and find that higher prediction confidence leads to lower estimation error. Guided by this analysis, we introduce a time-scheduled self-distillation loss during training that enhances prediction confidence in later training stages, thereby enabling more accurate probability estimation and improved convergence. Experiments show that \emph{d}-TreeRPO outperforms existing baselines and achieves significant gains on multiple reasoning benchmarks, including +86.2 on Sudoku, +51.6 on Countdown, +4.5 on GSM8K, and +5.3 on Math500. Ablation studies and computational cost analyses further demonstrate the effectiveness and practicality of our design choices.

Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting framework, we show that standard DDPMs induce a fundamental \emph{spectral collapse}: a Fourier-space analysis of the forward SDE reveals a closed-form, mode-wise signal-to-noise ratio (SNR) that decays monotonically in wavenumber, $|k|$ for spectra $S(k)\!\propto\!|k|^{-\lambda}$, rendering high-wavenumber modes indistinguishable from noise and producing an intrinsic spectral bias. We reinterpret the noise schedule as a spectral regularizer and introduce power-law schedules $\beta(\tau)\!\propto\!\tau^\gamma$ that preserve fine-scale structure deeper into diffusion time, along with \emph{Lazy Diffusion}, a one-step distillation method that leverages the learned score geometry to bypass long reverse-time trajectories and prevent high-$k$ degradation. Applied to high-Reynolds-number 2D Kolmogorov turbulence and $1/12^\circ$ Gulf of Mexico ocean reanalysis, these methods resolve spectral collapse, stabilize long-horizon autoregression, and restore physically realistic inertial-range scaling. Together, they show that naïve Gaussian scheduling is structurally incompatible with power-law physics and that physics-aware diffusion processes can yield accurate, efficient, and fully probabilistic surrogates for multiscale dynamical systems.