# ECE-TTS: A Zero-Shot Emotion Text-to-Speech Model with Simplified and Precise Control
## 2 Ece-Tts
### Modeling Principles  
#### 2.1.1 Flow Matching-Based TTS  
In recent years, Flow Matching (FM) [53] has been widely adopted in image generation tasks. Its core idea is to guide samples from a prior distribution to a target data distribution through time-dependent vector fields in the latent space, thereby enabling efficient generative modeling. Compared to traditional diffusion-based approaches, FM eliminates the need for score function estimation or complex numerical solvers, significantly improving generation efficiency while maintaining comparable synthesis quality. This modeling paradigm has also been extended to speech generation. Voicebox [54], proposed by Meta, is the first to apply Conditional Flow Matching (CFM) to speech synthesis, particularly targeting speech-infilling tasks. In Voicebox, the model is trained to reconstruct missing audio segments given partial speech context and a frame-level phoneme sequence as conditions. By combining masking strategies with conditional vector field supervision, Voicebox achieves natural and fluent speech generation in multilingual, cross-speaker, and even zero-shot settings. These results demonstrate the effectiveness and generalizability of CFM in sequential and condition-aware generation scenarios, offering a novel perspective for continuous modeling in TTS. Although speech and image data differ significantly in modality and structure, their generative processes can both be abstracted as continuous mappings from a noise distribution to a target distribution. As a result, the unified generation trajectory modeled by FM exhibits strong cross-modal transferability. In the speech domain, acoustic features such as Mel-spectrograms can be treated as continuous points in latent space, where their evolution is guided by time-dependent vector fields. Unlike image generation, which emphasizes local spatial structure, speech synthesis demands strict temporal coherence and semantic alignment with textual inputs. Inspired by the modeling principles of Voicebox, this work adopts Flow Matching as the core training objective, incorporating both textual and emotional representations as conditional inputs. Furthermore, we employ the Optimal Transport variant of CFM (OT-CFM) to constrain the generative trajectory between the prior and target distributions, enabling stable training while supporting fine-grained control over speaking style and emotional expression. This framework captures temporal dependencies along the entire generative path under conditional guidance, effectively enhancing the model's ability to produce natural and expressive speech. The flow matching loss function is defined in Equation (1), where the objective is to predict the expected behavior of the flow transformation given an input \(x_{0}\). The term \(u_{t}(x)\) represents the expected flow direction vector  
Our objective is to generate data samples that conform to the target distribution while starting from a simple distribution such as Gaussian noise. In this process, flow matching provides a vector field:  
\[\frac{d}{dt}\psi_{t}(x_{0})=u_{t}(\psi_{t}(x_{0})\mid x_{1}), \tag{4}\]  
By applying reparameterization, we derive the conditional flow matching loss function:  
\[L_{CFM}\left(\theta\right) = E_{t,q(x_{1}),\,p(x_{0})}\,\bigg{\|}\,v_{t}\left(\psi_{t}\left(x _{0}\right)\right)\,-\,\frac{d}{dt}\,\psi_{t}\left(x_{0}\right)\bigg{\|}^{2}, \tag{5}\]  
Utilizing the Optimal Transport (OT) formulation \(\psi_{t}(x)=(1-t)x+tx_{1}\), we can further express the OT-CFM loss function as follows:  
\[L_{CFM}\left(\theta\right) = E_{t,q(x_{1}),\,p(x_{0})}\,\|v_{t}((1-t)x_{0}+tx_{1})-(x_{1}-x_ {0})\|^{2}, \tag{6}\]  
During the inference stage, given a sample point \(x_{0}\) from the initial distribution, we solve for the flow's time step \(t\) and generation constraints using an Ordinary Differential Equation (ODE) solver [55]. The integral result of \(\psi_{t}(x_{0})\) is then evaluated as a function of time, with the initial condition set as \(\psi_{0}(x_{0})=x_{0}\).