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Physics-based differentiable rendering has emerged as a powerful technique in computer graphics and vision, with a broad range of applications in solving inverse rendering tasks. At its core, differentiable rendering enables the computation of gradients with respect to scene parameters, allowing optimization-based approaches to solve various problems. Over the past few years, significant advancements have been made in both the underlying theory and the practical implementations of differentiable rendering algorithms. In this report, we provide a comprehensive overview of the current state of the art in physics-based differentiable rendering, focusing on recent advances in general differentiable rendering theory, Monte Carlo sampling strategy, and computational efficiency.

While differentiable control has emerged as a powerful paradigm combining model-free flexibility with model-based efficiency, the iterative Linear Quadratic Regulator (iLQR) remains underexplored as a differentiable component. The scalability of differentiating through extended iterations and horizons poses significant challenges, hindering iLQR from being an effective differentiable controller. This paper introduces DiLQR, a framework that facilitates differentiation through iLQR, allowing it to serve as a trainable and differentiable module, either as or within a neural network. A novel aspect of this framework is the analytical solution that it provides for the gradient of an iLQR controller through implicit differentiation, which ensures a constant backward cost regardless of iteration, while producing an accurate gradient. We evaluate our framework on imitation tasks on famous control benchmarks. Our analytical method demonstrates superior computational performance, achieving up to 128x speedup and a minimum of 21x speedup compared to automatic differentiation. Our method also demonstrates superior learning performance ($10^6$x) compared to traditional neural network policies

Although integral-field spectroscopy enables spatially resolved spectral studies of galaxies, bridging particle-based simulations to observations remains slow and non-differentiable. We present RUBIX, a JAX-based pipeline that models mock integral-field unit (IFU) cubes for galaxies end-to-end and calculates gradients with respect to particle inputs. Our implementation is purely functional, sharded, and differentiable throughout. We validate the gradients against central finite differences and demonstrate gradient-based parameter estimation on controlled setups. While current experiments are limited to basic test cases, they demonstrate the feasibility of differentiable forward modelling of IFU data. This paves the way for future work scaling up to realistic galaxy cubes and enabling machine learning workflows for IFU-based inference. The source code for the RUBIX software is publicly available under https://github.com/AstroAI-Lab/rubix.

Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming paradigm enables end-to-end differentiation of complex computer programs (including those with control flows and data structures), making gradient-based optimization of program parameters possible. As an emerging paradigm, differentiable programming builds upon several areas of computer science and applied mathematics, including automatic differentiation, graphical models, optimization and statistics. This book presents a comprehensive review of the fundamental concepts useful for differentiable programming. We adopt two main perspectives, that of optimization and that of probability, with clear analogies between the two. Differentiable programming is not merely the differentiation of programs, but also the thoughtful design of programs intended for differentiation. By making programs differentiable, we inherently introduce probability distributions over their execution, providing a means to quantify the uncertainty associated with program outputs.

Three-dimensional rigid-body transforms, i.e. rotations and translations, are central to modern differentiable machine learning pipelines in robotics, vision, and simulation. However, numerically robust and mathematically correct implementations, particularly on SO(3), are error-prone due to issues such as axis conventions, normalizations, composition consistency and subtle errors that only appear in edge cases. SciPy's spatial$.$transform module is a rigorously tested Python implementation. However, it historically only supported NumPy, limiting adoption in GPU-accelerated and autodiff-based workflows. We present a complete overhaul of SciPy's spatial$.$transform functionality that makes it compatible with any array library implementing the Python array API, including JAX, PyTorch, and CuPy. The revised implementation preserves the established SciPy interface while enabling GPU/TPU execution, JIT compilation, vectorized batching, and differentiation via native autodiff of the chosen backend. We demonstrate how this foundation supports differentiable scientific computing through two case studies: (i) scalability of 3D transforms and rotations and (ii) a JAX drone simulation that le

AlphaFold 3 represents a transformative advancement in computational biology, enhancing protein structure prediction through novel multi-scale transformer architectures, biologically informed cross-attention mechanisms, and geometry-aware optimization strategies. These innovations dramatically improve predictive accuracy and generalization across diverse protein families, surpassing previous methods. Crucially, AlphaFold 3 embodies a paradigm shift toward differentiable simulation, bridging traditional static structural modeling with dynamic molecular simulations. By reframing protein folding predictions as a differentiable process, AlphaFold 3 serves as a foundational framework for integrating deep learning with physics-based molecular

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal transport-based differentiable Sinkhorn sorting algorithms to making classic sorting networks differentiable. One problem of current differentiable sorting methods is that they are non-monotonic. To address this issue, we propose a novel relaxation of conditional swap operations that guarantees monotonicity in differentiable sorting networks. We introduce a family of sigmoid functions and prove that they produce differentiable sorting networks that are monotonic. Monotonicity ensures that the gradients always have the correct sign, which is an advantage in gradient-based optimization. We demonstrate that monotonic differentiable sorting networks improve upon previous differentiable sorting methods.

Radiative transfer is a key bottleneck in computational astrophysics: it is nonlocal, stiff, and tightly coupled to hydrodynamics. We introduce Ray-trax, a GPU-oriented, fully differentiable 3D ray tracer written in JAX that solves the time-dependent emission--absorption problem and runs directly on turbulent gas fields produced by hydrodynamic simulations. The method favors the widely used on-the-fly emission--absorption approximation, which is state of the art in many production hydro codes when scattering is isotropic. Ray-trax vectorizes across rays and sources, supports arbitrarily many frequency bins without architectural changes, and exposes end-to-end gradients, making it straightforward to couple with differentiable hydro solvers while preserving differentiability. We validate against analytical solutions, demonstrate propagation in turbulent media, and perform a simple inverse problem via gradient-based optimization. In practice, the memory footprint scales as $\mathcal{O}(N_{\text{src}}\,N_{\text{cells}})$ while remaining highly efficient on accelerators.

We present a multi-scale differentiable brain modeling workflow utilizing BrainPy, a unique differentiable brain simulator that combines accurate brain simulation with powerful gradient-based optimization. We leverage this capability of BrainPy across different brain scales. At the single-neuron level, we implement differentiable neuron models and employ gradient methods to optimize their fit to electrophysiological data. On the network level, we incorporate connectomic data to construct biologically constrained network models. Finally, to replicate animal behavior, we train these models on cognitive tasks using gradient-based learning rules. Experiments demonstrate that our approach achieves superior performance and speed in fitting generalized leaky integrate-and-fire and Hodgkin-Huxley single neuron models. Additionally, training a biologically-informed network of excitatory and inhibitory spiking neurons on working memory tasks successfully replicates observed neural activity and synaptic weight distributions. Overall, our differentiable multi-scale simulation approach offers a promising tool to bridge neuroscience data across electrophysiological, anatomical, and behavioral sc

We present a differentiable extension of the VEROS ocean model, enabling automatic differentiation through its dynamical core. We describe the key modifications required to make the model fully compatible with JAX autodifferentiation framework and evaluate the numerical consistency of the resulting implementation. Two illustrative applications are then demonstrated: (i) the correction of an initial ocean state through gradient-based optimization, and (ii) the calibration of unknown physical parameters directly from model observations. These examples highlight how differentiable programming can facilitate end-to-end learning and parameter tuning in ocean modeling. Our implementation is available online.

We show how shadows can be efficiently generated in differentiable rendering of triangle meshes. Our central observation is that pre-filtered shadow mapping, a technique for approximating shadows based on rendering from the perspective of a light, can be combined with existing differentiable rasterizers to yield differentiable visibility information. We demonstrate at several inverse graphics problems that differentiable shadow maps are orders of magnitude faster than differentiable light transport simulation with similar accuracy -- while differentiable rasterization without shadows often fails to converge.

Inverse rendering seeks to reconstruct both geometry and spatially varying BRDFs (SVBRDFs) from captured images. To address the inherent ill-posedness of inverse rendering, basis BRDF representations are commonly used, modeling SVBRDFs as spatially varying blends of a set of basis BRDFs. However, existing methods often yield basis BRDFs that lack intuitive separation and have limited scalability to scenes of varying complexity. In this paper, we introduce a differentiable inverse rendering method that produces interpretable basis BRDFs. Our approach models a scene using 2D Gaussians, where the reflectance of each Gaussian is defined by a weighted blend of basis BRDFs. We efficiently render an image from the 2D Gaussians and basis BRDFs using differentiable rasterization and impose a rendering loss with the input images. During this analysis-by-synthesis optimization process of differentiable inverse rendering, we dynamically adjust the number of basis BRDFs to fit the target scene while encouraging sparsity in the basis weights. This ensures that the reflectance of each Gaussian is represented by only a few basis BRDFs. This approach enables the reconstruction of accurate geometry

Modelling how shocks propagate in supply chains is an increasingly important challenge in economics. Its relevance has been highlighted in recent years by events such as Covid-19 and the Russian invasion of Ukraine. Agent-based models (ABMs) are a promising approach for this problem. However, calibrating them is hard. We show empirically that it is possible to achieve speed ups of over 3 orders of magnitude when calibrating ABMs of supply networks by running them on GPUs and using automatic differentiation, compared to non-differentiable baselines. This opens the door to scaling ABMs to model the whole global supply network.

Autonomous drones capable of interpreting and executing high-level language instructions in unstructured environments remain a long-standing goal. Yet existing approaches are constrained by their dependence on hand-crafted skills, extensive parameter tuning, or computationally intensive models unsuitable for onboard use. We introduce GRaD-Nav++, a lightweight Vision-Language-Action (VLA) framework that runs fully onboard and follows natural-language commands in real time. Our policy is trained in a photorealistic 3D Gaussian Splatting (3DGS) simulator via Differentiable Reinforcement Learning (DiffRL), enabling efficient learning of low-level control from visual and linguistic inputs. At its core is a Mixture-of-Experts (MoE) action head, which adaptively routes computation to improve generalization while mitigating forgetting. In multi-task generalization experiments, GRaD-Nav++ achieves a success rate of 83% on trained tasks and 75% on unseen tasks in simulation. When deployed on real hardware, it attains 67% success on trained tasks and 50% on unseen ones. In multi-environment adaptation experiments, GRaD-Nav++ achieves an average success rate of 81% across diverse simulated env

In this paper, using the tools from the lineability theory, we distinguish certain subsets of $p$-adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional algebraic structure: (i) continuously differentiable but not strictly differentiable functions, (ii) strictly differentiable functions of order $r$ but not strictly differentiable of order $r+1$, (iii) strictly differentiable functions with zero derivative that are not Lipschitzian of any order $α>1$, (iv) differentiable functions with unbounded derivative, and (v) continuous functions that are differentiable on a full set with respect to the Haar measure but not differentiable on its complement having cardinality the continuum.

Differentiable simulators provide analytic gradients, enabling more sample-efficient learning algorithms and paving the way for data intensive learning tasks such as learning from images. In this work, we demonstrate that locomotion policies trained with analytic gradients from a differentiable simulator can be successfully transferred to the real world. Typically, simulators that offer informative gradients lack the physical accuracy needed for sim-to-real transfer, and vice-versa. A key factor in our success is a smooth contact model that combines informative gradients with physical accuracy, ensuring effective transfer of learned behaviors. To the best of our knowledge, this is the first time a real quadrupedal robot is able to locomote after training exclusively in a differentiable simulation.

Building differentiable simulations of physical processes has recently received an increasing amount of attention. Specifically, some efforts develop differentiable robotic physics engines motivated by the computational benefits of merging rigid body simulations with modern differentiable machine learning libraries. Here, we present a library that focuses on the ability to combine data driven methods with analytical rigid body computations. More concretely, our library \emph{Differentiable Robot Models} implements both \emph{differentiable} and \emph{learnable} models of the kinematics and dynamics of robots in Pytorch. The source-code is available at \url{https://github.com/facebookresearch/differentiable-robot-model}

Laser-enabled selective transfer, a key process in high-throughput microLED fabrication, requires computational models that can plan shift sequences to minimize motion of XY stages and adapt to varying optimization objectives across the substrate. We propose the first repair algorithm based on a differentiable transfer module designed to model discrete shifts of transfer platforms, while remaining trainable via gradient-based optimization. Compared to local proximity searching algorithms, our approach achieves superior repair performance and enables more flexible objective designs, such as minimizing the number of steps. Unlike reinforcement learning (RL)-based approaches, our method eliminates the need for handcrafted feature extractors and trains significantly faster, allowing scalability to large arrays. Experiments show a 50% reduction in transfer steps and sub-2-minute planning time on 2000x2000 arrays. This method provides a practical and adaptable solution for accelerating microLED repair in AR/VR and next-generation display fabrication.