This paper studies the identifiability and stability of drifting fields within the framework of Generative Modeling via Drifting. The motivating question is whether a zero-drift equilibrium identifies the target distribution, and whether an approximate zero drift implies weak distributional convergence. Since the original drifting model employs the Laplace kernel by default, we first analyze why standard Gaussian score-based arguments fail to apply. This analysis motivates the introduction of companion-elliptic kernel families, which are characterized by a companion potential satisfying an elliptic closure relation. We show that this class naturally contains the Laplace kernel and consists precisely of Gaussian and Matérn kernels with smoothness parameter $ν\ge 1/2$. Within this class, we establish field identifiability for arbitrary Borel probability measures on $\mathbb{R}^d$: if the drifting field vanishes identically, then the two measures must coincide. As for stability, we demonstrate that field convergence alone does not guarantee weak convergence, since mass may escape to infinity while remaining invisible to the field. Although tightness of the sequence directly removes this obstruction and restores weak stability, we prove that, even without tightness, every $C_0$-vague cluster point lies exactly on the defect ray $\{cp:0\le c\le1\}$. Consequently, a single scalar $C_0$-observable suffices to detect the missing mass and recover weak convergence.

While it has been the subject of several recent theoretical studies, many important questions related to adversarial robustness are still open.

Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles.

A.2 MainProofsketch In this section we will give a theoretical guarantee for the performance of our algorithm. Essentially, it measures the largest total difference of value estimation among all the functions in f Ft for the fixed inputsxt,i wherei [M]. Lemma 2. If (βt 0 | t N) is a nondecreasing sequence and Ft:=n Themainstructure ofthisproof issimilar toproposition 3,section CinEluder dimension's paper, and we will only point out the subtle details that makes the difference. Apart from the notations section 3, we add more symbols for the regret analysis. Next, we will show thatf h is a feasible solution for the optimization ofFt.