By embedding discrete representations into a continuous latent space, we can leverage continuous-space latent diffusion models to handle generative modeling of discrete data. However, despite their initial success, most latent diffusion methods rely on fixed pretrained embeddings, limiting the benefits of joint training with the diffusion model. While jointly learning the embedding (via reconstruction loss) and the latent diffusion model (via score matching loss) could enhance performance, end-to-end training risks embedding collapse, degrading generation quality. To mitigate this issue, we introduce VQ-LCMD, a continuous-space latent diffusion framework within the embedding space that stabilizes training. VQ-LCMD uses a novel training objective combining the joint embedding-diffusion variational lower bound with a consistency-matching (CM) loss, alongside a shifted cosine noise schedule and random dropping strategy. Experiments on several benchmarks show that the proposed VQ-LCMD yields superior results on FFHQ, LSUN Churches, and LSUN Bedrooms compared to discrete-state latent diffusion models. In particular, VQ-LCMD achieves an FID of 6.81 for class-conditional image generation on ImageNet with 50 steps.