Jonathan Ho

Chenlin Meng, Robin Rombach, Ruiqi Gao et al. · deepmind

Classifier-free guided diffusion models have recently been shown to be highly effective at high-resolution image generation, and they have been widely used in large-scale diffusion frameworks including DALLE-2, Stable Diffusion and Imagen. However, a downside of classifier-free guided diffusion models is that they are computationally expensive at inference time since they require evaluating two diffusion models, a class-conditional model and an unconditional model, tens to hundreds of times. To deal with this limitation, we propose an approach to distilling classifier-free guided diffusion models into models that are fast to sample from: Given a pre-trained classifier-free guided model, we first learn a single model to match the output of the combined conditional and unconditional models, and then we progressively distill that model to a diffusion model that requires much fewer sampling steps. For standard diffusion models trained on the pixel-space, our approach is able to generate images visually comparable to that of the original model using as few as 4 sampling steps on ImageNet 64x64 and CIFAR-10, achieving FID/IS scores comparable to that of the original model while being up to 256 times faster to sample from. For diffusion models trained on the latent-space (e.g., Stable Diffusion), our approach is able to generate high-fidelity images using as few as 1 to 4 denoising steps, accelerating inference by at least 10-fold compared to existing methods on ImageNet 256x256 and LAION datasets. We further demonstrate the effectiveness of our approach on text-guided image editing and inpainting, where our distilled model is able to generate high-quality results using as few as 2-4 denoising steps.

Jonathan Ho, William Chan, Chitwan Saharia et al. · deepmind

We present Imagen Video, a text-conditional video generation system based on a cascade of video diffusion models. Given a text prompt, Imagen Video generates high definition videos using a base video generation model and a sequence of interleaved spatial and temporal video super-resolution models. We describe how we scale up the system as a high definition text-to-video model including design decisions such as the choice of fully-convolutional temporal and spatial super-resolution models at certain resolutions, and the choice of the v-parameterization of diffusion models. In addition, we confirm and transfer findings from previous work on diffusion-based image generation to the video generation setting. Finally, we apply progressive distillation to our video models with classifier-free guidance for fast, high quality sampling. We find Imagen Video not only capable of generating videos of high fidelity, but also having a high degree of controllability and world knowledge, including the ability to generate diverse videos and text animations in various artistic styles and with 3D object understanding. See https://imagen.research.google/video/ for samples.

Chitwan Saharia, William Chan, Saurabh Saxena et al. · deepmind

We present Imagen, a text-to-image diffusion model with an unprecedented degree of photorealism and a deep level of language understanding. Imagen builds on the power of large transformer language models in understanding text and hinges on the strength of diffusion models in high-fidelity image generation. Our key discovery is that generic large language models (e.g. T5), pretrained on text-only corpora, are surprisingly effective at encoding text for image synthesis: increasing the size of the language model in Imagen boosts both sample fidelity and image-text alignment much more than increasing the size of the image diffusion model. Imagen achieves a new state-of-the-art FID score of 7.27 on the COCO dataset, without ever training on COCO, and human raters find Imagen samples to be on par with the COCO data itself in image-text alignment. To assess text-to-image models in greater depth, we introduce DrawBench, a comprehensive and challenging benchmark for text-to-image models. With DrawBench, we compare Imagen with recent methods including VQ-GAN+CLIP, Latent Diffusion Models, and DALL-E 2, and find that human raters prefer Imagen over other models in side-by-side comparisons, both in terms of sample quality and image-text alignment. See https://imagen.research.google/ for an overview of the results.

Daniel Watson, William Chan, Ricardo Martin-Brualla et al. · deepmind

We present 3DiM, a diffusion model for 3D novel view synthesis, which is able to translate a single input view into consistent and sharp completions across many views. The core component of 3DiM is a pose-conditional image-to-image diffusion model, which takes a source view and its pose as inputs, and generates a novel view for a target pose as output. 3DiM can generate multiple views that are 3D consistent using a novel technique called stochastic conditioning. The output views are generated autoregressively, and during the generation of each novel view, one selects a random conditioning view from the set of available views at each denoising step. We demonstrate that stochastic conditioning significantly improves the 3D consistency of a naive sampler for an image-to-image diffusion model, which involves conditioning on a single fixed view. We compare 3DiM to prior work on the SRN ShapeNet dataset, demonstrating that 3DiM's generated completions from a single view achieve much higher fidelity, while being approximately 3D consistent. We also introduce a new evaluation methodology, 3D consistency scoring, to measure the 3D consistency of a generated object by training a neural field on the model's output views. 3DiM is geometry free, does not rely on hyper-networks or test-time optimization for novel view synthesis, and allows a single model to easily scale to a large number of scenes.

Jonathan Ho, Tim Salimans · deepmind

Classifier guidance is a recently introduced method to trade off mode coverage and sample fidelity in conditional diffusion models post training, in the same spirit as low temperature sampling or truncation in other types of generative models. Classifier guidance combines the score estimate of a diffusion model with the gradient of an image classifier and thereby requires training an image classifier separate from the diffusion model. It also raises the question of whether guidance can be performed without a classifier. We show that guidance can be indeed performed by a pure generative model without such a classifier: in what we call classifier-free guidance, we jointly train a conditional and an unconditional diffusion model, and we combine the resulting conditional and unconditional score estimates to attain a trade-off between sample quality and diversity similar to that obtained using classifier guidance.

Jonathan Ho, Tim Salimans, Alexey Gritsenko et al.

Generating temporally coherent high fidelity video is an important milestone in generative modeling research. We make progress towards this milestone by proposing a diffusion model for video generation that shows very promising initial results. Our model is a natural extension of the standard image diffusion architecture, and it enables jointly training from image and video data, which we find to reduce the variance of minibatch gradients and speed up optimization. To generate long and higher resolution videos we introduce a new conditional sampling technique for spatial and temporal video extension that performs better than previously proposed methods. We present the first results on a large text-conditioned video generation task, as well as state-of-the-art results on established benchmarks for video prediction and unconditional video generation. Supplementary material is available at https://video-diffusion.github.io/

Amazon AGI, Aaron Langford, Aayush Shah et al. · amazon-science

We present Amazon Nova, a new generation of state-of-the-art foundation models that deliver frontier intelligence and industry-leading price performance. Amazon Nova Pro is a highly-capable multimodal model with the best combination of accuracy, speed, and cost for a wide range of tasks. Amazon Nova Lite is a low-cost multimodal model that is lightning fast for processing images, video, documents and text. Amazon Nova Micro is a text-only model that delivers our lowest-latency responses at very low cost. Amazon Nova Canvas is an image generation model that creates professional grade images with rich customization controls. Amazon Nova Reel is a video generation model offering high-quality outputs, customization, and motion control. Our models were built responsibly and with a commitment to customer trust, security, and reliability. We report benchmarking results for core capabilities, agentic performance, long context, functional adaptation, runtime performance, and human evaluation.

Diederik P. Kingma, Tim Salimans, Ben Poole et al.

Diffusion-based generative models have demonstrated a capacity for perceptually impressive synthesis, but can they also be great likelihood-based models? We answer this in the affirmative, and introduce a family of diffusion-based generative models that obtain state-of-the-art likelihoods on standard image density estimation benchmarks. Unlike other diffusion-based models, our method allows for efficient optimization of the noise schedule jointly with the rest of the model. We show that the variational lower bound (VLB) simplifies to a remarkably short expression in terms of the signal-to-noise ratio of the diffused data, thereby improving our theoretical understanding of this model class. Using this insight, we prove an equivalence between several models proposed in the literature. In addition, we show that the continuous-time VLB is invariant to the noise schedule, except for the signal-to-noise ratio at its endpoints. This enables us to learn a noise schedule that minimizes the variance of the resulting VLB estimator, leading to faster optimization. Combining these advances with architectural improvements, we obtain state-of-the-art likelihoods on image density estimation benchmarks, outperforming autoregressive models that have dominated these benchmarks for many years, with often significantly faster optimization. In addition, we show how to use the model as part of a bits-back compression scheme, and demonstrate lossless compression rates close to the theoretical optimum. Code is available at https://github.com/google-research/vdm .

Jonathan Ho, Ajay Jain, Pieter Abbeel

We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics. Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding. On the unconditional CIFAR10 dataset, we obtain an Inception score of 9.46 and a state-of-the-art FID score of 3.17. On 256x256 LSUN, we obtain sample quality similar to ProgressiveGAN. Our implementation is available at https://github.com/hojonathanho/diffusion

Jonathan Ho, Nal Kalchbrenner, Dirk Weissenborn et al.

We propose Axial Transformers, a self-attention-based autoregressive model for images and other data organized as high dimensional tensors. Existing autoregressive models either suffer from excessively large computational resource requirements for high dimensional data, or make compromises in terms of distribution expressiveness or ease of implementation in order to decrease resource requirements. Our architecture, by contrast, maintains both full expressiveness over joint distributions over data and ease of implementation with standard deep learning frameworks, while requiring reasonable memory and computation and achieving state-of-the-art results on standard generative modeling benchmarks. Our models are based on axial attention, a simple generalization of self-attention that naturally aligns with the multiple dimensions of the tensors in both the encoding and the decoding settings. Notably the proposed structure of the layers allows for the vast majority of the context to be computed in parallel during decoding without introducing any independence assumptions. This semi-parallel structure goes a long way to making decoding from even a very large Axial Transformer broadly applicable. We demonstrate state-of-the-art results for the Axial Transformer on the ImageNet-32 and ImageNet-64 image benchmarks as well as on the BAIR Robotic Pushing video benchmark. We open source the implementation of Axial Transformers.

Friso H. Kingma, Pieter Abbeel, Jonathan Ho

The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models, however, is still an open problem. Bits-Back with Asymmetric Numeral Systems (BB-ANS), recently proposed by Townsend et al. (2019), makes bits-back coding practically feasible for latent variable models with one latent layer, but it is inefficient for hierarchical latent variable models. In this paper we propose Bit-Swap, a new compression scheme that generalizes BB-ANS and achieves strictly better compression rates for hierarchical latent variable models with Markov chain structure. Through experiments we verify that Bit-Swap results in lossless compression rates that are empirically superior to existing techniques. Our implementation is available at https://github.com/fhkingma/bitswap.

Jonathan Ho, Xi Chen, Aravind Srinivas et al.

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at https://github.com/aravindsrinivas/flowpp

Daniel Watson, William Chan, Jonathan Ho et al.

Diffusion models have emerged as an expressive family of generative models rivaling GANs in sample quality and autoregressive models in likelihood scores. Standard diffusion models typically require hundreds of forward passes through the model to generate a single high-fidelity sample. We introduce Differentiable Diffusion Sampler Search (DDSS): a method that optimizes fast samplers for any pre-trained diffusion model by differentiating through sample quality scores. We also present Generalized Gaussian Diffusion Models (GGDM), a family of flexible non-Markovian samplers for diffusion models. We show that optimizing the degrees of freedom of GGDM samplers by maximizing sample quality scores via gradient descent leads to improved sample quality. Our optimization procedure backpropagates through the sampling process using the reparametrization trick and gradient rematerialization. DDSS achieves strong results on unconditional image generation across various datasets (e.g., FID scores on LSUN church 128x128 of 11.6 with only 10 inference steps, and 4.82 with 20 steps, compared to 51.1 and 14.9 with strongest DDPM/DDIM baselines). Our method is compatible with any pre-trained diffusion model without fine-tuning or re-training required.

Tim Salimans, Jonathan Ho

Diffusion models have recently shown great promise for generative modeling, outperforming GANs on perceptual quality and autoregressive models at density estimation. A remaining downside is their slow sampling time: generating high quality samples takes many hundreds or thousands of model evaluations. Here we make two contributions to help eliminate this downside: First, we present new parameterizations of diffusion models that provide increased stability when using few sampling steps. Second, we present a method to distill a trained deterministic diffusion sampler, using many steps, into a new diffusion model that takes half as many sampling steps. We then keep progressively applying this distillation procedure to our model, halving the number of required sampling steps each time. On standard image generation benchmarks like CIFAR-10, ImageNet, and LSUN, we start out with state-of-the-art samplers taking as many as 8192 steps, and are able to distill down to models taking as few as 4 steps without losing much perceptual quality; achieving, for example, a FID of 3.0 on CIFAR-10 in 4 steps. Finally, we show that the full progressive distillation procedure does not take more time than it takes to train the original model, thus representing an efficient solution for generative modeling using diffusion at both train and test time.

Chitwan Saharia, William Chan, Huiwen Chang et al.

This paper develops a unified framework for image-to-image translation based on conditional diffusion models and evaluates this framework on four challenging image-to-image translation tasks, namely colorization, inpainting, uncropping, and JPEG restoration. Our simple implementation of image-to-image diffusion models outperforms strong GAN and regression baselines on all tasks, without task-specific hyper-parameter tuning, architecture customization, or any auxiliary loss or sophisticated new techniques needed. We uncover the impact of an L2 vs. L1 loss in the denoising diffusion objective on sample diversity, and demonstrate the importance of self-attention in the neural architecture through empirical studies. Importantly, we advocate a unified evaluation protocol based on ImageNet, with human evaluation and sample quality scores (FID, Inception Score, Classification Accuracy of a pre-trained ResNet-50, and Perceptual Distance against original images). We expect this standardized evaluation protocol to play a role in advancing image-to-image translation research. Finally, we show that a generalist, multi-task diffusion model performs as well or better than task-specific specialist counterparts. Check out https://diffusion-palette.github.io for an overview of the results.

Jacob Austin, Daniel D. Johnson, Jonathan Ho et al.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Daniel Watson, Jonathan Ho, Mohammad Norouzi et al.

Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a powerful family of generative models that can yield high-fidelity samples and competitive log-likelihoods across a range of domains, including image and speech synthesis. Key advantages of DDPMs include ease of training, in contrast to generative adversarial networks, and speed of generation, in contrast to autoregressive models. However, DDPMs typically require hundreds-to-thousands of steps to generate a high fidelity sample, making them prohibitively expensive for high dimensional problems. Fortunately, DDPMs allow trading generation speed for sample quality through adjusting the number of refinement steps as a post process. Prior work has been successful in improving generation speed through handcrafting the time schedule by trial and error. We instead view the selection of the inference time schedules as an optimization problem, and introduce an exact dynamic programming algorithm that finds the optimal discrete time schedules for any pre-trained DDPM. Our method exploits the fact that ELBO can be decomposed into separate KL terms, and given any computation budget, discovers the time schedule that maximizes the training ELBO exactly. Our method is efficient, has no hyper-parameters of its own, and can be applied to any pre-trained DDPM with no retraining. We discover inference time schedules requiring as few as 32 refinement steps, while sacrificing less than 0.1 bits per dimension compared to the default 4,000 steps used on ImageNet 64x64 [Ho et al., 2020; Nichol and Dhariwal, 2021].

Jonathan Ho, Chitwan Saharia, William Chan et al.

We show that cascaded diffusion models are capable of generating high fidelity images on the class-conditional ImageNet generation benchmark, without any assistance from auxiliary image classifiers to boost sample quality. A cascaded diffusion model comprises a pipeline of multiple diffusion models that generate images of increasing resolution, beginning with a standard diffusion model at the lowest resolution, followed by one or more super-resolution diffusion models that successively upsample the image and add higher resolution details. We find that the sample quality of a cascading pipeline relies crucially on conditioning augmentation, our proposed method of data augmentation of the lower resolution conditioning inputs to the super-resolution models. Our experiments show that conditioning augmentation prevents compounding error during sampling in a cascaded model, helping us to train cascading pipelines achieving FID scores of 1.48 at 64x64, 3.52 at 128x128 and 4.88 at 256x256 resolutions, outperforming BigGAN-deep, and classification accuracy scores of 63.02% (top-1) and 84.06% (top-5) at 256x256, outperforming VQ-VAE-2.

Chitwan Saharia, Jonathan Ho, William Chan et al.

We present SR3, an approach to image Super-Resolution via Repeated Refinement. SR3 adapts denoising diffusion probabilistic models to conditional image generation and performs super-resolution through a stochastic denoising process. Inference starts with pure Gaussian noise and iteratively refines the noisy output using a U-Net model trained on denoising at various noise levels. SR3 exhibits strong performance on super-resolution tasks at different magnification factors, on faces and natural images. We conduct human evaluation on a standard 8X face super-resolution task on CelebA-HQ, comparing with SOTA GAN methods. SR3 achieves a fool rate close to 50%, suggesting photo-realistic outputs, while GANs do not exceed a fool rate of 34%. We further show the effectiveness of SR3 in cascaded image generation, where generative models are chained with super-resolution models, yielding a competitive FID score of 11.3 on ImageNet.

Wilson Yan, Jonathan Ho, Pieter Abbeel

Deep autoregressive models are one of the most powerful models that exist today which achieve state-of-the-art bits per dim. However, they lie at a strict disadvantage when it comes to controlled sample generation compared to latent variable models. Latent variable models such as VAEs and normalizing flows allow meaningful semantic manipulations in latent space, which autoregressive models do not have. In this paper, we propose using Fisher scores as a method to extract embeddings from an autoregressive model to use for interpolation and show that our method provides more meaningful sample manipulation compared to alternate embeddings such as network activations.

Jonathan Ho, Evan Lohn, Pieter Abbeel

Likelihood-based generative models are the backbones of lossless compression due to the guaranteed existence of codes with lengths close to negative log likelihood. However, there is no guaranteed existence of computationally efficient codes that achieve these lengths, and coding algorithms must be hand-tailored to specific types of generative models to ensure computational efficiency. Such coding algorithms are known for autoregressive models and variational autoencoders, but not for general types of flow models. To fill in this gap, we introduce local bits-back coding, a new compression technique for flow models. We present efficient algorithms that instantiate our technique for many popular types of flows, and we demonstrate that our algorithms closely achieve theoretical codelengths for state-of-the-art flow models on high-dimensional data.

Rein Houthooft, Richard Y. Chen, Phillip Isola et al.

We propose a metalearning approach for learning gradient-based reinforcement learning (RL) algorithms. The idea is to evolve a differentiable loss function, such that an agent, which optimizes its policy to minimize this loss, will achieve high rewards. The loss is parametrized via temporal convolutions over the agent's experience. Because this loss is highly flexible in its ability to take into account the agent's history, it enables fast task learning. Empirical results show that our evolved policy gradient algorithm (EPG) achieves faster learning on several randomized environments compared to an off-the-shelf policy gradient method. We also demonstrate that EPG's learned loss can generalize to out-of-distribution test time tasks, and exhibits qualitatively different behavior from other popular metalearning algorithms.

Kevin Frans, Jonathan Ho, Xi Chen et al.

We develop a metalearning approach for learning hierarchically structured policies, improving sample efficiency on unseen tasks through the use of shared primitives---policies that are executed for large numbers of timesteps. Specifically, a set of primitives are shared within a distribution of tasks, and are switched between by task-specific policies. We provide a concrete metric for measuring the strength of such hierarchies, leading to an optimization problem for quickly reaching high reward on unseen tasks. We then present an algorithm to solve this problem end-to-end through the use of any off-the-shelf reinforcement learning method, by repeatedly sampling new tasks and resetting task-specific policies. We successfully discover meaningful motor primitives for the directional movement of four-legged robots, solely by interacting with distributions of mazes. We also demonstrate the transferability of primitives to solve long-timescale sparse-reward obstacle courses, and we enable 3D humanoid robots to robustly walk and crawl with the same policy.

Yan Duan, Marcin Andrychowicz, Bradly C. Stadie et al.

Imitation learning has been commonly applied to solve different tasks in isolation. This usually requires either careful feature engineering, or a significant number of samples. This is far from what we desire: ideally, robots should be able to learn from very few demonstrations of any given task, and instantly generalize to new situations of the same task, without requiring task-specific engineering. In this paper, we propose a meta-learning framework for achieving such capability, which we call one-shot imitation learning. Specifically, we consider the setting where there is a very large set of tasks, and each task has many instantiations. For example, a task could be to stack all blocks on a table into a single tower, another task could be to place all blocks on a table into two-block towers, etc. In each case, different instances of the task would consist of different sets of blocks with different initial states. At training time, our algorithm is presented with pairs of demonstrations for a subset of all tasks. A neural net is trained that takes as input one demonstration and the current state (which initially is the initial state of the other demonstration of the pair), and outputs an action with the goal that the resulting sequence of states and actions matches as closely as possible with the second demonstration. At test time, a demonstration of a single instance of a new task is presented, and the neural net is expected to perform well on new instances of this new task. The use of soft attention allows the model to generalize to conditions and tasks unseen in the training data. We anticipate that by training this model on a much greater variety of tasks and settings, we will obtain a general system that can turn any demonstrations into robust policies that can accomplish an overwhelming variety of tasks. Videos available at https://bit.ly/nips2017-oneshot .

Tim Salimans, Jonathan Ho, Xi Chen et al.

We explore the use of Evolution Strategies (ES), a class of black box optimization algorithms, as an alternative to popular MDP-based RL techniques such as Q-learning and Policy Gradients. Experiments on MuJoCo and Atari show that ES is a viable solution strategy that scales extremely well with the number of CPUs available: By using a novel communication strategy based on common random numbers, our ES implementation only needs to communicate scalars, making it possible to scale to over a thousand parallel workers. This allows us to solve 3D humanoid walking in 10 minutes and obtain competitive results on most Atari games after one hour of training. In addition, we highlight several advantages of ES as a black box optimization technique: it is invariant to action frequency and delayed rewards, tolerant of extremely long horizons, and does not need temporal discounting or value function approximation.

Jonathan Ho, Stefano Ermon

Consider learning a policy from example expert behavior, without interaction with the expert or access to reinforcement signal. One approach is to recover the expert's cost function with inverse reinforcement learning, then extract a policy from that cost function with reinforcement learning. This approach is indirect and can be slow. We propose a new general framework for directly extracting a policy from data, as if it were obtained by reinforcement learning following inverse reinforcement learning. We show that a certain instantiation of our framework draws an analogy between imitation learning and generative adversarial networks, from which we derive a model-free imitation learning algorithm that obtains significant performance gains over existing model-free methods in imitating complex behaviors in large, high-dimensional environments.

Jonathan Ho, Jayesh K. Gupta, Stefano Ermon

In imitation learning, an agent learns how to behave in an environment with an unknown cost function by mimicking expert demonstrations. Existing imitation learning algorithms typically involve solving a sequence of planning or reinforcement learning problems. Such algorithms are therefore not directly applicable to large, high-dimensional environments, and their performance can significantly degrade if the planning problems are not solved to optimality. Under the apprenticeship learning formalism, we develop alternative model-free algorithms for finding a parameterized stochastic policy that performs at least as well as an expert policy on an unknown cost function, based on sample trajectories from the expert. Our approach, based on policy gradients, scales to large continuous environments with guaranteed convergence to local minima.