diff --git a/ggml/src/ggml-cuda/mmq.cu b/ggml/src/ggml-cuda/mmq.cu
index e1cf843de1a65..2db5b4ab0f09c 100644
--- a/ggml/src/ggml-cuda/mmq.cu
+++ b/ggml/src/ggml-cuda/mmq.cu
@@ -122,6 +122,7 @@ void ggml_cuda_mul_mat_q(
             const int64_t s13 = src1->nb[3] / ts_src1;
             quantize_mmq_q8_1_cuda(src1_d, nullptr, src1_q8_1.get(), src0->type,
                 ne10, s11, s12, s13, ne10_padded, ne11, ne12, ne13, stream);
+            CUDA_CHECK(cudaGetLastError());
         }
 
         const int64_t s12 = ne11*ne10_padded * sizeof(block_q8_1)/(QK8_1*sizeof(int));
@@ -205,6 +206,7 @@ void ggml_cuda_mul_mat_q(
         const int64_t s13 = src1->nb[2] / ts_src1;
         quantize_mmq_q8_1_cuda(src1_d, ids_src1_dev, src1_q8_1.get(), src0->type,
             ne10, s11, s12, s13, ne10_padded, ne11_flat, ne12_flat, ne13_flat, stream);
+        CUDA_CHECK(cudaGetLastError());
     }
 
     const int64_t s12 = ne11*ne10_padded * sizeof(block_q8_1)/(QK8_1*sizeof(int));
diff --git a/ggml/src/ggml-cuda/quantize.cu b/ggml/src/ggml-cuda/quantize.cu
index cb93181455d47..a0b03a740d74c 100644
--- a/ggml/src/ggml-cuda/quantize.cu
+++ b/ggml/src/ggml-cuda/quantize.cu
@@ -56,13 +56,13 @@ static __global__ void quantize_mmq_q8_1(
     constexpr int vals_per_scale = ds_layout == MMQ_Q8_1_DS_LAYOUT_D2S6 ? 64 : 32;
     constexpr int vals_per_sum   = ds_layout == MMQ_Q8_1_DS_LAYOUT_D2S6 ? 16 : 32;
 
-    const int64_t i0 = ((int64_t)blockDim.x*blockIdx.x + threadIdx.x)*4;
+    const int64_t i0 = ((int64_t)blockDim.x*blockIdx.y + threadIdx.x)*4;
 
     if (i0 >= ne0) {
         return;
     }
 
-    const int64_t i1 = blockIdx.y;
+    const int64_t i1 = blockIdx.x;
     const int64_t i2 = blockIdx.z % ne2;
     const int64_t i3 = blockIdx.z / ne2;
 
@@ -75,8 +75,8 @@ static __global__ void quantize_mmq_q8_1(
 
     block_q8_1_mmq * y = (block_q8_1_mmq *) vy;
 
-    const int64_t ib0 = blockIdx.z*((int64_t)gridDim.y*gridDim.x*blockDim.x/QK8_1); // first block of channel
-    const int64_t ib  = ib0 + (i0 / (4*QK8_1))*ne1 + blockIdx.y;                    // block index in channel
+    const int64_t ib0 = blockIdx.z*((int64_t)gridDim.x*gridDim.y*blockDim.x/QK8_1); // first block of channel
+    const int64_t ib  = ib0 + (i0 / (4*QK8_1))*ne1 + blockIdx.x;                    // block index in channel
     const int64_t iqs = i0 % (4*QK8_1);                                             // quant index in block
 
     // Load 4 floats per thread and calculate max. abs. value between them:
@@ -166,8 +166,9 @@ void quantize_mmq_q8_1_cuda(
     GGML_ASSERT(ne00 % 4 == 0);
     GGML_ASSERT(ne0 % (4*QK8_1) == 0);
 
-    const int64_t block_num_x = (ne0 + 4*CUDA_QUANTIZE_BLOCK_SIZE_MMQ - 1) / (4*CUDA_QUANTIZE_BLOCK_SIZE_MMQ);
-    const dim3 num_blocks(block_num_x, ne1, ne2*ne3);
+    // ne1 tends to assume the highest values, therefore use it as the "x" dimension of the CUDA grid:
+    const int64_t block_num_y = (ne0 + 4*CUDA_QUANTIZE_BLOCK_SIZE_MMQ - 1) / (4*CUDA_QUANTIZE_BLOCK_SIZE_MMQ);
+    const dim3 num_blocks(ne1, block_num_y, ne2*ne3);
     const dim3 block_size(CUDA_QUANTIZE_BLOCK_SIZE_MMQ, 1, 1);
     switch (mmq_get_q8_1_ds_layout(type_src0)) {
         case MMQ_Q8_1_DS_LAYOUT_D4: